Multihop Packet Radio Sytems in Rough Terrain en... · computer communications in a mobile...

KUNGL TEKNISKA HÖGSKOLAN Royal Institute of Technology

Multihop Packet Radio Sytems in Rough Terrain

OSCAR SOMARRIBA

DEPARTMENT OF SIGNALS, SENSORS AND SYSTEMS

RADIO COMMUNICATION SYSTEMS

KUNGL TEKNISKA HÖGSKOLAN Royal Institute of Technology

Multihop Packet Radio Sytems in Rough Terrain

OSCAR SOMARRIBA Licentiate Thesis October 95 TRITA-S3-RST-9506 ISSN 1400-9137 ISRN KTH/RST/R-- 95/06 --SE

DEPARTMENT OF SIGNALS, SENSORS AND SYSTEMS

RADIO COMMUNICATION SYSTEMS

Abstract

Multihop Packet Radio Networks (PRN:s) offer interesting possibilities for reliable rural data communications in areas where no "external" telecommunication infrastructure is present. One key design issue in PRN:s is the formulation of Medium Access Control (MAC) protocols. In this thesis, the performance for two MAC protocols, Slotted ALOHA (S-ALOHA) and Spatial TDMA (S-TDMA), is investigated in multihop PRN:s. A detailed radio propagation model, which takes the terrain shadowing into account is used. A finite number of buffered nodes were used in the evaluation of these two MAC protocols. Optimum network performance is achieved when the average packet delay is minimized. For S-ALOHA, nodes transmit at random with some given probability q. For this protocol, we investigate the selection of q. An assignment for transmission probability is given in terms of the traffic load and the connectivity, which yields a near optimal network performance. Furthermore, a novel systematic procedure to find transmission schedules in S-TDMA based on the gain matrix is described. The traffic-sensitive schedules show better performance in comparison to the classical S-TDMA. Also, the results from sample networks suggest that there is a favorable connectivity for this protocol, i.e., 3.2 -3.4 neighbors in a network with ten nodes. As expected, S-ALOHA works well with low traffic loads. For high loads, S-TDMA exhibits better performance. Lastly, we explore how we can affect the connectivity by changing the transmitted power and the antenna height, and their respective influences on the network performance. It turns out that S-ALOHA is less sensitive to these changes than S-TDMA.

Ackowledgment My debt is to my supervisor Professor Jens Zander, Radio Communicattions Systems, Royal Institute of Technology, for his guidance as well as inspiration and encouragement he has provided throughout this thesis work. Without his outsatanding support this work would not has been possible. It has been an enriching experience to work at the Radio Communications Systems, because of that I would like to express my sisncere gratitude to my friends and colleagues in this Group. Especially, I would like to tahnk Dr. Bo hagerman for valuable discussion and sugestions. Lise-Lotte Walhberg should be thanked for all help in practical aspects regarding the completion of this work. I also thank Dr. Magnus Frodigh at Ericsson Radio Systems AB for valuable comments on the manuscript. The financial support from the Swedish Agency for Research with Developing Countries (SAREC) is gartefully ackowledged. Lastly, I would like to express my gartitude to Virginia, for her love and support. Stockholm, October 1995 Oscar Somarriba

Contents 1 Introduction_______________________________________________________1

1.1 Multihop Packet Radio Communication Systems __________________________1

1.2 Today’s applications of multihop PRN:s_________________________________2

1.3 Literature review ____________________________________________________3

1.4 Outline of the thesis__________________________________________________7

2 Systems Models ___________________________________________________9

2.1 Models ___________________________________________________________9 2.1.1 Network model _______________________________________________________ 9

2.1.2 Terrain model _________________________________________________________ 10

2.1.3 Path loss model _______________________________________________________ 12

2.1.4 Connectivity model ____________________________________________________ 17

2.1.5 Routing Algorithms____________________________________________________ 20

2.1.6 Traffic model _________________________________________________________ 23

2.2 Performance Measure ______________________________________________26

2.3 Performance Evaluation ____________________________________________28

3 Slotted ALOHA ___________________________________________________31

3.1 Slotted ALOHA protocols in multihop environment_______________________31

3.2 Slotted ALOHA with constant transmission probability policy ______________40

3.3 Slotted ALOHA for node adaptive transmission probability policy___________43

4 Spatial TDMA ___________________________________________________47

4.1 Spatial TDMA in multihop scenarios __________________________________47

4.2 Network delay of conventional spatial TDMA ___________________________54

4.3 Traffic-sensitive spatial TDMA_______________________________________59

4.4 Comparison of S- ALOHA and S-TDMA_______________________________64

5 Some Implementation Aspects ____________________________________67

5.1 Network performance versus transmitter power __________________________67

5.2 Network performance versus antenna height ____________________________71

5.3 Practical aspects ___________________________________________________72

6 Conclusions and discussion _______________________________________75

References___________________________________________________________79

Appendix A Performance evaluation ______________________________________83

Appendix B Slotted ALOHA support ______________________________________87

Appendix C Spatial TDMA support _______________________________________89 Appendix D Samples Nets ______________________________________________ 93

Chapter 1 Introduction Current wireless systems, such as cellular radio system, are supported by a tethered infrastructure of fixed base stations linked by a wired network. In some cases, such as with emergency disaster relief, the wired network is not available and this type of architecture is not feasible. Moreover, we might face the challenge of providing communications in rural areas or sparsely populated areas where no wired network exists. A very attractive alternative for data communication in areas without a wired telecommunication infrastructure is to use autonomous radio networks. These networks allow for wireless communications between a ”changing” number of network entities in the situation were no ”external” infrastructure is present. Moreover, such wireless networks could be suitable for military and emergency applications, mobile users, low density personal systems, surveillance of critical signals and remote data acquisition. 1.1 Multihop Packet Radio Communication Systems One type of autonomous radio networks is the multihop Packet Radio Networks (PRN:s). PRN:s emerged as applications of packet switching techniques to a shared radio channel and are intended to support communications between users over a wide-spread geographical area where a line connection is difficult or impossible. In addition, they also support mobile users and access to a mobile subnet. They usually carry packets of data between nodes equipped with radio transceivers and omnidirectional antennas [1]. With the decrease in the cost of a packet radio unit [2], PRN:s have become a practical way of providing communications. In many PRN:s, not all packet radio nodes can communicate directly because of interference, range limitations, or natural obstacles. In this situation, a packet transferred between two distant nodes may have to be relayed by intermediate stations or nodes. Major design issues in PRN:s involve the "path finding" methods, i.e. the routing algorithms, and the protocols that determine which nodes share the channel to transmit their packets (Figure 1.1). Also, the transmitted power and directional antennas have been addressed as important parameters in the design of PRN:s.

1

packet

Next node?

When to transmit ?

To attached device

path of the packet

Multihop Packet Radio Network

Node

computer

data logger

Packet

Figure 1.1 MAC protocols and Routing algorithms in PRN:s.

In a multihop network, a message may travel long distances by means of a store-and-forward mechanism: a node transmits to another node, which in turn forwards the packet. This procedure is repeated until the packet arrives at its final destination. In each retransmission phase, the node currently holding the message uses the network routing algorithm to determine the next node in the transmission chain. In an adverse environment where links and nodes may fail without prior warning, nodes cannot rely on routing information distributed from a central routing information distribution center ("station" [1]). Instead, nodes need to make their routing decisions based on limited knowledge about their immediate surroundings. In addition to making a routing decisions, each node needs to determine when a message is to be transmitted to the neighboring node selected by the routing scheme. This decision is governed by the Medium Access Control (MAC) protocol (or multiple access protocol). Since transmissions in different links in the network may interfere with one another, the routing and access procedures are strongly interconnected [3,5,6]. The goal of the combined routing and access schemes is primarily to minimize the end-to-end packet delay, i.e., the time that it takes a packet to travel from the source station to the final destination station. Often (but not always), this goal coincides with maximizing the number of packets successfully transported through the network, the packet throughput. 1.2 Today’s applications of multihop PRN:s Data packet technology was developed in the mid-1960’s and was put into practical application in the ARPANET in 1969. The first large-scale PR project, ALOHANET [7],

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based at the University of Hawaii became operational in 1970. Its principal objective was to allow user terminals in widely scattered locations to access the university computer system. Since ALOHANET, many PRN:s have been implemented, some of them in the multihop fashion such as: 1) DARPA PRNET. Since 1973, the US Defense Advanced Research Projects Agency (DARPA) initiated research on the feasibility of using packet-switched techniques, store and forward radio communications to provide reliable computer communications. As a result of these, the DARPA Packet Radio Network (PRNET) has evolved to provide computer communications in a mobile environment [22]. Also, in 1983, DARPA has sponsored the Survivable, Adaptive Networks (SURAN) program [23] to research and develop network technology capable of supporting communication between computers and their users in the modern battlefield. In the last program, spread spectrum techniques are used. To support experimentation with and demonstration of the advance, adaptive channel capability, the Low-cost Packet Radio Unit (LPR) was developed [2], with 180 LPR:s having been produced up until 1990 [23]. This constitutes a PRN for military communication. 2) AMATEUR PRN. It is worthwhile mentioning the experiments of the radio amateurs which has lead to a standard for the level-link protocol suitable for packet radio networks known as AX.25 [24-25] sponsored by the American Radio Relay League (ARRL). An ARRL-type network is a distributed network organized into clusters of stations connected by repeaters with fixed routing. Amateur PRN began in Montreal, Canada in 1978. This was followed by the Vancouver Amateur Digital Communications Group (VADG) development of a Terminal Node Controller (TNC) in 1980. The improved versions of this TCN provide the ”work horses” of today’s amateur PRN:s. This technology is used all around the world and provides an experimental platform for the amateur community. Also, PRN of this kind have been suggested as ”cheap” means of studying digital radio communications and an attractive possibility for providing emergency communication in case of natural disasters. 1.3 Literature review Several MAC protocols have been proposed in the literature, and in [4] an overview of the existing multiple access protocols is given. They can be grouped into at least four classes: • Fixed assignment protocols • Random access protocols

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• Demand assignment protocols • Adaptive assignment protocols. The protocols in the first class, fixed assignment protocols, dedicate a fixed portion of the available channel capacity to each user. Examples of this type of protocol are the FDMA (Frequency Division Multiple Access), TDMA (Time Division Multiple Access) and CDMA (Code Division Multiple Access). Conversely, in random access (contention) protocols, the entire bandwidth is presented to the users as a single channel to be accessed randomly. This means that collisions (an overlapping in time of messages sent by two or more different stations) of messages can occur, and that colliding messages must be retransmitted. Common forms of this class are S-ALOHA (Slotted ALOHA) [8], and CSMA (Carrier Sense Multiple Access) [37]. Alternately, demand assignment techniques require that explicit control information concerning the users’ need for channel capacity is exchanged. The control can be either centralized or distributed; in a centralized scheme a central controller exists that decides which user should next have access to the channel, whereas in a distributed scheme, each user monitors the requests from other users to determine who next has channel access. In both schemes, the control information is exchanged through the channel, which leads to additional overhead [13-15]. The final class of MAC protocols, mentioned above, are the adaptive assignment schemes. So far, these have not been studied as extensively as the other schemes. Here, the access method can change according to the traffic load of the users, with the objective being to achieve near optimal performance at all times. However, the overhead incurred can often outweigh the advantages. In this thesis, we consider two MAC protocols: slotted ALOHA and spatial TDMA. In some sense these, two protocols represent two extremes among all the multiple access protocols. In the slotted ALOHA protocol, no attempt is made to coordinate the access of the nodes to the channel, while in the spatial TDMA protocol, every station is designated to transmit in some predetermined timeslot(s). In spatial TDMA, the "collision" problem is totally eliminated by adopting a link activation mechanism that is conflict-free and can thus guarantee a finite time for message transmission [35]. The earliest MAC protocol in PRN:s was the one-hop centralized pure ALOHA first described by Abramson in [7]. With the pure ALOHA protocol, a station transmits whenever it has a packet to send, with no coordination with other stations sharing the

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channel, thus leaving the possibility for collisions. Thanks to feedback mechanisms, stations may rapidly know if the packet transmission resulted in a collision or not. Once a transmitting station detects a collision, it retransmits the packet after a random amount of time. In general, the packet throughput provided by the pure ALOHA is not very high due to collisions and idle periods in the channel. To improve efficiency, a modification of pure ALOHA, slotted ALOHA, was developed that divided the channel into time slots. For the MAC protocol, nodes transmit at random with some given probability, q. This access scheme and collision mechanism has been investigated by Roberts [8]. In the new algorithm, stations are allowed to transmit packets only at the start of a time slot. By this modification, the probability of ”overlapping” decreases and therefore resulting in an improvement of network performance and doubling the packet throughput of the original ALOHA protocol. With the collision one attractive feature exists that even when packets do collide, it may still be possible to receive the strongest packet if the power ratio of this packets to other packets, is above a certain threshold. In this situation we say that the receiver 'captures' this packet. This threshold is called the protection ratio. To further improve network performance, other random channel access protocols, e.g., Carrier Sense Multiple Access (CSMA), have been proposed [37]. We now concentrate on some MAC protocols for the multihop scenario. The most popular topic in the literature has been the slotted ALOHA multihop networks. The performance of the slotted ALOHA protocol in a multihop environment has been studied in [3] and [6] and, the optimum transmission range in planar networks of randomly distributed nodes determined. Resulting from the packet throughput analysis, it has been suggested that the selection of q be 0.113 [3]. A more exact analysis involving several routing algorithms with power adaptation is given by Hou and Li [5]. Moreover, in [5-6] it was found that the optimal number of neighbors, is in the range 6 to 8. In [10], Nelson and Kleinrock have refined the analysis presented in [6], but with capture effect and a different routing algorithm. Shiao and Yee [11] have investigated the determination of global optimal routing assignment and the transmission probabilities to maximize the end-to-end throughput. Their end-to-end throughput showed an increase of approximately 45 % in comparison with the results in [9], where the capacity of some multihop radio networks with regular structure using the slotted ALOHA random access protocol is studied. Since random MAC protocols exhibit comparatively poor performance in high load situations; "conflict-free" multiple access have been proposed to ensure that a transmission, whenever made, is successful. That is, a packet transmission is not disturbed

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by another transmission. In [12], the channel access protocol spatial TDMA for multihop PRN:s is proposed. The term spatial refers to the spatial reuse property of the radio networks, i.e., multiple nodes may be allowed to transmit simultaneous as long as they do not "interfere" with one another. The key point in spatial reuse is that when a node is transmitting in some part, it is possible to reuse the same frequency and time in another part of the network with no (significant) interference. This effect is due either to the propagation loss or the fact that one part of the network is shielded from other areas, i.e. terrain shadowing (perhaps by natural obstacles such as mountains or by the nature of radio propagation). When the node locations are fixed and known, transmissions are scheduled such that only non-interfering links are used simultaneously. Also in [12], an approximated analysis for the average packet delay was performed. In 1989, Cidon and Sidi [13] proposed two distributed algorithms for multihop PRN:s: the round-robin algorithm where the nodes priorities are cycled; and the wait-for-neighbors algorithm where assigned nodes are eliminated from the following slot assignment procedure before all neighboring nodes are assigned. In the last algorithm, whenever a node is assigned to transmit in a slot, it does not participate in the slot assignment procedure in the posterior slots, until it hears that all its neighnbours have been assigned at least once, and only then it resumes its participation in the slot assignment procedure.These two algorithms ensure conflict-free transmissions by the nodes of the network. In 1990, Ephremides and Troung [14] proposed centralized and distributed algorithms to find a maximal schedule where each node is assigned at each time slot diagonally; nodes with higher priorities are assigned in the remaining timeslots. Robertazzi and Shor also described traffic-sensitive algorithms for the generation of schedules [15], in particular, a distributed degree algorithm that is, a "traffic-sensitized" version of the algorithm developed in [14]. Literature surveys about the modeling and performance analysis of multihop PRN:s can be found in [20-21]. In earlier studies, very simple connectivity based transmission models were used. The network is described by its connectivity matrix. Two nodes are assumed to be connected if a two-way radio link of sufficient quality can be established. In the random networks investigated, this could include all stations within a certain radius. A transmitting station is assumed to interfere with the reception of a packet if it is connected with the receiving station. Thus, the connectivity matrix contains all the information about connectivity and interference [3,12,13]. However, this view yields very pessimistic results since even weakly received signals are assumed to interfere regardless of the signal strength of the desired signal. The phenomenon that a strong signal may be "captured" by the receiver that suppresses interference was included in later models [6,8]. In [16], this model is

6

refined and the Signal-to-Interference Ratio at the receiver is used to determine whether packets are lost or not. In these studies a simple distance dependent propagation-loss model was used, corresponding to isotropic propagation over a smooth earth. This appears to be a pessimistic assumption as well, since studies have shown that signal strength variations (fading) may in fact improve the performance of the network [17]. In [18], a random network was studied in a random terrain taking distance loss as well as shadowing losses in a "typical" terrain into account and it was shown that the r model [19], used in former studies, yields pessimistic results in predicting the network connectivity. Moreover, the use of ”realistic” propagation models for predicting the network connectivity which incorporate the effects of irregular terrain (e.g., diffraction of mountains) has been completely ignored in most of the analytical performance studies in radio networks of this kind.

−α

1.4 Outline of the thesis One drawback with the performance formulation in the literature studies is that the existing models consider only part of the PRN functions, thereby making analysis tractable [21]. Furthermore, most of the studies of MAC protocols in multihop PRN:s have been performed using oversimplified propagation models despite the current availability of powerful radio propagation models. To further enrich our basic understanding of PRN:s, we propose a more integrated approach [36], that incorporates a detailed propagation model [19,27-28] with simple nodal queueing. With this new modeling of multihop PRN:s we are able to include most of the relevant factors in computing the network connectivity, we are able to better model interference and identify what impact these factors have on network performance. In order to include the actual radio propagation aspect useful for a "realistic" model, parameters such as path loss and radio range are needed. To calculate these parameters, we can probably get the data base of a particular map terrain or use prediction techniques to accurately predict coverage in specific locations [27]. In our study we create a synthetic (random) terrain, which allow us to use the same methodology as if it were a real terrain to calculate the radio influence on network performance. One of the most important performance measures that strongly influence the choice and performance of network algorithms [26], is the average packet delay required to deliver a packet from origin to destination. This work examines the delay associated with two multiple access schemes, studying "refined" slotted ALOHA protocols [3-11,16,18,36] and spatial TDMA protocols [12-15,30,34-36]. The modeling mentioned above is used and analysis is largely based on computer simulations, since the intricate interference

7

8

patterns existing in this unique environment are extremely difficult to capture in an tractable analytical model. The work is restricted to a single frequency which is assigned for use by the node in ground radio networks. The thesis is organized as follows. Chapter 2 introduces the models and assumptions used for performance analysis of the MAC protocols concerned, while Chapter 3 illustrates the type of results obtained for multihop slotted ALOHA protocols. A near optimal transmission probability assignment is presented which minimized the network delay. Chapter 4 is devoted to the spatial TDMA protocols, where new ways of creating transmission schedules are proposed. In Chapter 5, the transmitter power and antenna height are used in sample networks to illustrate their impact on the network connectivity. Finally, Chapter 6 discusses the results and some conclusions.

Chapter 2 System Models This chapter introduces the performance analysis used in this thesis and consists of three main parts: the models, the performance measure, and the ”measurement” methodology. 2.1 Models The following models for studying network performance for multihop PRN:s, are presented: the network model, the terrain model, the path loss model, the connectivity model, the routing algorithms and the traffic model. 2.1.1 Network model To study MAC protocols one must make preliminaries definitions regarding the environment in which they operate. Here, we will often refer to the following issues [43]: • Radio channel is medium through which data is transferred from its source to its

destination. This channel uses electromagnetic propagation in open space. • Radio link is the one-way communication between a transmitter and a receiver through

the radio channel, where the signal at the receiver has an acceptable quality that will be defined later. Throughout the thesis, the term radio link is often shortened to link.

• Connectivity, in a broad sense, is the ability of a node to hear the transmission of

another nodes. A more detailed discussion about our connectivity model is found in Section 2.1.4.

• Collision is a situation in which, at the receiver, two or more transmissions overlap in

time. Typically, a PRN consists of a collection of nodes that communicate with each other through the radio channel. Theses nodes are geographically spread out over a given area. Traditionally [26], the topology of a PRN can be represented by a graph as in Fig. 2.1. The graph, G = (N, L), contains a set of nodes N and a set of radio links, L. Each radio link in L corresponds to an ordered pair of nodes, i.e. (i,j), and indicates that transmission from i

9

1

2

34

5

6

7

Legend: # , Node #, Two radio links

Figure 2.1 Connectivity graph of a PRN of seven nodes (N =7) and 20 links.

can be heard with an adequate signal energy at j. Shortly, under this condition we say that (i,j) L. Moreover, in Figure 2.1 each edge denotes two radio links, one in each direction, i.e., (i,j) is one link and (j,i) is another link. So, we assume that if (i,j,) ∈ L, then the (j,i)

L. Also, Figure 2.1 is often named the connectivity graph of a PRN. Since the connectivity depends on many factors (e.g., the transmitted power) we will introduce them before.

∈

∈

However, in real life systems one cannot ignore the scenario, i.e. the terrain, in which we consider our PRN:s will be placed. Furthermore, the terrain shadowing has a great influence in the radio communication among the nodes. Thus, to make use of most of the input parameters that affect radio propagation we introduce our terrain model. 2.1.2 Terrain model The terrain height variations are generated by a slightly modified version of a stationary two-dimensional random process as proposed in [18]. Let H(x,y) denote the height at location (x,y). H(x,y) is generated by:

H x y H x k y l p k llk

( , ) ( , ) ( , )*= − − ⋅=−=−∑∑

ρ

ρ

ρ

ρ

(2.1)

where H*(x,y) is a two-dimensional white Gaussian process with zero mean and variance (height parameter), and p(x,y) can be seen as the impulse response of a filter, given by :

σ

10

Figure 2.2 Computer plot and contour plot of a terrain realization. Both x and y axes are 2 km. Heights vary in this realization between 300 and 800 m. The terrain parameters are:

= 40 m, 8

σ ρ = 3 m.

p x y

x y y( , )

cos ( (( ) ( )

)) ( ), ( )=

+ ⋅+

+−

≤ + ≤ −

11 1

1 1

0

2

2

2

2πρ ρ

ρ ρ x

otherwise

(2.2)

ρ can be referred to as the smoothness parameter in meters. In Figure 2.2, one terrain realization is shown. Here, the terrain parameters are = 40 meters and σ ρ =3 meters. Heights vary between 300 and 800 meters, and the area is 28x28 . A realization of this kind is regarded, in this context as a "rough" terrain, that mimics a real scenario for a radio network. In Table 2.1 we have, as an example, given a few combinations of the terrain parameters.

km2

Type of terrain height parameter (σ in m ) smoothness param. ( in m) ρ mountainous σ ≥ 25 2 > > 20 ρ undulating 1 > σ > 25 2 > > 20 ρ smooth or ‘flat’ σ 0 ≈ 20 ρ ≥

Table 2.1 Simple classification of different terrain types according to our model.

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2.1.3 Path loss model

The mechanisms which govern radio propagation are complex and diverse, and they can generally be attributed to three basic propagation mechanisms: reflection, diffraction, and scattering. Reflection occurs when a propagating electromagnetic wave impinges on an obstacle with dimensions very large compared to the wavelength of the radio wave. Reflections from the surface of the earth produces reflected waves that may interfere constructively or destructively at the receiving site. Diffraction, on the other hand, occurs when the radio path between the transmitter and receiver is obstructed by an impenetrable object, and the obstacle encountered is not large compared with the operating radio wavelength. Based on Huygens´ principle, we can model propagation phenomena by introducing secondary waves that are formed behind the obstructing object even though a line-of-sight (LOS) between the transmitter and receiver does not exits. Thus, diffraction can be regarded as the ”bending” of radio waves around the edge of an obstruction [31]. The scattering mechanism, finally, is not considered in our models. It is well known that radio signals are attenuated as they propagate from the transmitter station to the receiver station. The main variation of the signal strength versus distance is described by a path loss term, which states the relation between the emitted power and the received signal strength for a given separation of the antennas. The prediction of path loss is a very important step in performance analysis, operation and/or design of multihop PRN:s. Throughout the thesis, we use the path loss prediction model by Ladell [19] where the loss due to the terrain can be split into three components: a distance dependent path loss, a plane-earth propagation loss, and a (multiple knife-edge) diffraction loss due to the mountains in our terrain model. We neglect the influence, for instance, of the vegetation in the terrain. With this detailed radio propagation model, it is possible to estimate the total propagation loss in each link, . Here we introduced the propagation loss , which is the ratio of the emitted signal in node i when the received signal in node j, is . Expressed in decibels, this becomes:

Lij

ansmitt

Lij

Ptr ed Preceived

( ) log (log ) (log )L L Pij dB ij transmitted received= ⋅ = ⋅ − ⋅10 10 1010 10 10 P (2.3a)

Moreover, the inverse of the propagation loss in link between the node i and j is the power gain [33] and it can be expressed as: Gij

G Lij ij= −( ) 1 (2.3b)

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A convenient way to indicate the power gain between each pair of nodes in the network is by means of the so-called gain matrix G [28]. The gain matrix might be described as G = , where is the power gain between node i and node j. {Gij } Gij

We briefly describe the path loss components of the radio prediction method mentioned above. Free space loss (distance depend) To calculate the propagation loss in dB due some distance d, we use the well-known formula (assuming a link between isotropic antennas) [31]:

L dfs = ⋅20 4

10log ( )πλ

(2.4)

where is the free space loss. Lfs

Modified flat earth propagation loss (plane-earth) For simplicity, we assume that the earth is modeled as a plain partially conducting surface. In other words for the moment, we momentarily neglect the roughness of the terrain and model the earth as a smooth sphere. In [19], a method to calculate the flat earth propagation loss the actual field strength relative to the free space strength if the ground conductivity is neglected. A typical communications link can be described by the geometry in Figure 2.2. T and R represent the transmitting and receiving sites, respectively.

L flat

The heights above the earth’s surface are (at the transmitting site in meters) and (at the receiving site in meters). in dB can be expressed

ht hr

L flat

L A Bflat t r= ⋅ ⋅ ⋅ + ⋅20 2 0 5 1 2log ( sin( . (( ) ( ) ) )/ + B)A (2.5) where

A (2.6)

hdt r

t r,

,=4 2π

λ

B Cd

=−

λπ ε( )1

(2.7)

(2.8) C =

ε 2

1

for vertical polarization

for horizontal polarization

13

Figure 2.3 Two mutually-visible antennas located above a smooth, spherical earth of

effective radius . Figure from [31]. Re

= wavelength, m ε = relative permittivity , λ d = distance between the two stations in meters. To use this former formula for the flat earth propagation loss, we need to take into account the curvature of the earth, by limiting distances to: d ≤ ⋅ ⋅12 103 1 3λ / (2.9) The earth curvature correction factor can be expressed as:

Yx

x x x=

− ⋅

+ ⋅ − ⋅ ≤ <

2 86 7 10 10 2 210

.. log .

x < 0.53 0.53

(2.10)

Here, we have introduced the normalized distance x as: x k Re= ⋅ −( / ) ( )/ /2 1 3 2 3π λ d⋅

Y

(2.11) where R earthe = effective radius, m = 6370 000 m k e arth= radius factor (4 / 3 for standard ratio atmosphere) In summary, the modified flat earth propagation loss, , can be written as: Lmflat

L Lmflat flat= + (2.12) Diffraction loss

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Propagation over rough terrain is often adversely affected by obstructions such as hilltops. Path loss resulting from such obstacles is termed ”diffraction loss”. Methods to calculate the multiple knife-edge diffraction can be found in [31-32]. The diffraction model used is based on the multiple knife-edge diffraction presented by Epstein-Peterson and refined by Ladell [19]. In order to calculate for a single knife-edge diffraction, first calculate the auxiliary parameter (refer to Figure 2.3.a): ν

v hd dd d

=+2 1 2

1 2

( )λ

(2.13)

Four parameters are needed to find the ν : , the distance from the transmitting antenna to the obstacle, h, the relative height of the knife-edge h, , the receiver distance away from the obstruction, and , the operating wavelength. When the value of is obtained, the diffraction loss due to a mountain can be found using the approximate formula below [19]:

d1

d 2

λ ν

L(d ,d , h) = dB 0 v 2.4

dB v 2.41 2

− − ⋅ + ⋅ ≤ <

− − ⋅ ≥

6 02 911 1 2712 95 20

2

10

. . .. log

v vv

(2.14)

However, in many instances, there is more than one knife-edge source along a given propagation loss between two antennas, in which case the loss may be estimated by the Epstein-Peterson method. This technique computes the attenuation due to each obstacle in turn and compute their sum obtain the overall diffraction loss. For example, let the path between the transmitting antenna to the receiving antenna contain three obstacles as shown in Figure 2.3.b. A line is drawn from the transmitting antenna to the top of the second mountain, and the loss due to first mountain is then calculated using the single knife-edge diffraction (formulas 2.13 and 2.14). The effective height of first mountain is -

, the height below the line from T to the second mountain. In a similar manner the attenuation due to the second mountain is determined by connecting the peaks of mountain 1 and 3 and using the height above that line as the effective height, , of the second mountain. Again we calculate the loss, in this case due to the second mountain, and we repeat the same procedure for the third mountain, i.e. the effective height h is computed using the line joining mountain 2 to the receiving antenna. The total diffraction loss , is then obtained by summing the individual losses due to each obstacle:

h1

h2

3

Ldri

Ldri = L( , ,- )+L( , , )+L( , , ) (2.15) d1 d 2 h1 d 2 d 3 h2 d 3 d 4 h3

15

h

d1 d2

Transmitting antenna

Obstacle

Receiving antenna

a.

b.

R

T

−h1

h2

h3

d1 d4d3d2

Figure 2.4 a. The (single) knife-edge diffraction model. b. The Epstein-Peterson (multiple knife-edge) diffraction construction.

Total path loss

The propagation loss is described by a model that combines the diffraction loss, , due to the mountains and the flat earth propagation, , [19]:

Ldri

Lmflat

L L Lc mflat dri= + 2 2

fs

dB (2.16)

It should be emphasized that there is no theoretical justification for combining the losses in the way indicated by (2.16). However, this empirical model has proved to be in good agreement with measurements performed in various types of irregular terrain in Sweden [19]. The total path loss, , can then be computed as: Lt

L L Lt c= + dB (2.17)

16

Finally, we now relate the power gain Gij, between node I and j, with the total path loss Lt in the link (i,j) as follows (see Figure 2.5):

t

rt

t

rij L

GGPP

==G (2.18)

where Pt = Transmitted power level (W or DBW) Pr = Received power level (W or DBW) Gt = Antenna gain (DB) at the transmitter site Gr = Antenna gain (DB) at the receiver site. We will assume that all the antennas are omnidirectiona in the azimuth plane, and we associate the antennas heights (Fig. 2.3) ht, hr to Gt and Gr, respectively.

Gij

Gt Gr

P Pr

t

Receiving Node j

Transmitting Node i

Lt

Figure 2.5 A radio link between node i and j. 2.1.4 Connectivity model In the terrain a network of N randomly uniformly distributed nodes will be considered. Nodes i and j, with i, j { }∈ are either connected by a link or disconnected, depending on the propagation loss between the nodes. The propagation effect is modeled by link gains where (inverse of propagation losses for the link concerned) denotes the power (propagation) gain on the link between nodes i and node j [28], and is derived from the terrain model. Note that even through the network, in principle, is fully connected, many links can be characterized by a very low gain (high loss) and establishing a communication link may not be possible if an adequate signal energy at the receiver is required. In the follows, we assume a simple connectivity model where if the propagation

1,2, . . . , N

Gij

17

loss in a given link (i,j) is larger than some threshold path loss, communication cannot be sustained, i.e., no connection exists along the link between node i and j. The threshold path loss is defined as the maximum path loss for which a communication link may be established in the absence of all interference. Computing the link budget [33], involve the calculations of the useful signal power, and noise power available at the receiver. One can regard as the link budget a ”balance sheet” of gains and losses. Moreover, the desired transmission is also received in the presence of network self-interference, which in turn, depends on the MAC protocol, the density of the network and the traffic load (see section 2.16). Therefore, the Signal-to-Interference-Ratio (SIR) is commonly used as a measure of the link quality. For a link (i,j) we introduce the SIR, , when node i transmits with power , to node j:

φ o

(PEI

Frec

P Gt

Γij

Pt

≤

o

t= ⋅

t iP GN I+

= ≤0γ

(2.19) ( ) Γij

j t

ij

PN I L

= =+

where N is the noise power, and I is the interference power. In order to have a reliable link a minimum SIR is required, referred to as the SIR threshold

or the SIR target. Moreover, to relate the SIR threshold and the φ mentioned above, we consider in Eqn. 2.19 the case when I=0: γ 0 γ 0 o

(2.20a) N φ Γij

t t r

o

P G G

or in dB ( )γ o dB + - ( - ( - - (2.20b) )RP dB ( )Gr dB )φ o dB )kTo dB ( )Frec dB ( )B dB

and where, φ o = threshold path loss N= k B T

PEIRP = The Efficient Isotropic Radiated Power k= Boltzmans constant =13 J/K 8 10 23. ⋅ −

To = reference temperature = 290 K. Frec = Noise Figure of the receiver. B= Bandwidth of the receiver in Hz.

18

Thus, in order to model the effect of the interference at a given receiving site, we consider a packet to be correctly received if its received signal exceeds the sum of the power of the other colliding packets by at least dB (capture property). When we consider the capture effect, a slotted access scheme is assumed and a packet from node i is successfully received at node j if the Signal-to-Interference-Ratio from Eqn. 2.19:

γ o

(2.21)

Γijt ij

kk i

i ij

kj k kk i

P GN I

P GN G X P

=+

=+

≠ ≠∑ ∑

is greater than the threshold , otherwise the packet is lost. Here we have introduced the

binary variable

γ o

Xk =

1

0

node k transmits

node k does not transmit (2.22)

and and , the transmitter power of station i and k respectively. Also, we remind that each node uses the same transmitter power. The former notation is used to distinguish between the desired transmission and the interferes at the receiving node j.

Pi PK

The threshold path loss on a given link between two nodes can be found from (2.20b):

( )φ o dB ≤ Pt + + - - ( - +204 (2.23) Gt Gr ( )γ o dB )Frec dB ( )B dB

For instance, by putting the following values in equation (2.23),

Pt = - 5 dBW, = 3 dB, ( = 10 dB, =15 dB, = 50 dB G Gt , r )γ o dB ( )Frec dB

( )B dB

we would have = 130 dB. It should be noted that we assume a bandwidth of 100 KHz, capable of supporting date rates around 100 Kbits/sec. This could be, for instance, a requirement for low rate data communications.

( )φ o dB

Figure 2.6 illustrates the same terrain with less contours as in Figure 2.2. Ten nodes (N=10) are placed on it, with the network connectivity depicted as well. We refer to this network as network A, with Figure 2.6 being its connectivity diagram. Sample network B is depicted in Figure 2.7. As mentioned earlier, we would like to have an idea of the

19

quality of our links in the network or the average number of ”good” connections, therefore, an important parameter in multihop PRN:s could be a measure of the network connectivity. For simplicity, we have chosen the average number of neighbors N for this purpose where neighbors to a transmitting station consist of all nodes within the transmission range according to our assumption of connection based on the path loss threshold. The parameter N is calculated as follows:

N = i=1 N iN∑ /N (2.24)

where is the number of neighbors to node i. From network A (Figure 2.6), it can be seen that

N i

N is equal to 3.2 nodes. In the same way, for network B, N = 4.2 nodes. In general, we can consider two kind of connected networks: partial connected network and fully connected network. Moreover, in a multihop PRN each node is connected to some subset of the other nodes. Thus, we say that a network is connected if there is a path between every node to reach every other node. By a path we mean a collection of node-to-node link connecting a given source to a given destination. Hence, to characterize our interest here in the effect of connectivity in PRN we might define in this context: Partially connected network: It is a PRN where every node cannot reach every other node in one hop and thus we do require a routing algorithm. Unless we stated the contrary, in this thesis, we refer to the partial connected network as a connected network. Fully connected network: It is a PRN where every node can reach every other node with reliable link quality in one hop and thus no explicit routing is required. In this case, = N-1, for every node i in the network.

N i

2.1.5 Routing Algorithms

In a multihop PRN, the function of the routing algorithm is to guide the packets through the radio network to their proper destination. Connections are made in such a way that between any given pair of nodes, there is at least one path available. In this structure, a packet needs to be relayed from node to node to reach its final recipient. If a given node has more than one outgoing link, it must make routing decisions, i.e., for every incoming packet, it must be decide on which outgoing link the packet will be relayed. For reasons of efficiency, a routing

20

5 10 15 20 25

5

10

15

20

25

distance in kilometers

dist

ance

in k

ilom

eter

s 12

3

4

5

6

7

8

9

10

Figure 2.6 Contour plot of the terrain and Network A. Terrain parameters are: = 40 m, σ ρ =

3 m. The circles indicate the position of the stations, which are numbered 1,2..10. The

lines represent the connections among the nodes.

5 10 15 20 25

5

10

15

20

25


dist

ance

in k

ilom

eter

s

1

2

3

46

5

7

8

9

10

Figure 2.7 Contour plot of the terrain and Network B. Terrain parameters are: = 40 m, σ ρ =

3 m. The circles indicate the position of the stations, which are numbered 1,2..10. The

lines represent the connections among the nodes.

21

node typically attempts to relay packets along paths of ”minimum” delay (i.e., the shortest paths) leading to their destinations. A few terrain adaptive routing schemes such as: the Minimum Hop Algorithm, the Minimum Maximum Path Loss algorithm, and the Minimum Interference algorithm were defined and investigated in [18]. As a result of the former study, it was observed that the expected numbers of hops increase with the increasing roughness of the terrain. The Minimum Hop and the Minimum Interference algorithms exhibited a similar network delay, both being better than the Minimum Maximum Path Loss algorithm. For this thesis, we use the Minimum Hop Algorithm (MHA) which searches between nodes i and j for the path with the minimum number of hops. Take for instance network B in Figure 2.7. To get a message from node 1 to node 10, the path that is taken will follow links (1,2), (2,3) and (3,10). If however the link (3,10) would not be there, there would be at least three paths, namely, path 1: (1,2), (2,3), (3,4), (4,10); path 2: (1,2), (2,3), (3,5), (5,10); and path 3: (1,2), (2,3), (3,7), (7,4), (4,10). With path 1, path 2 and path 3, a packet takes 4 hops, 4 hops and 5 hops to reach the intended receiver, respectively. So first, the MHA would choose path 1 and path 2 due to they offer fewer number of hops than path 3. Besides, the number of hops in the two reminder paths is the same. In this case one of the two is chosen randomly. Actually, the MHA count the number of hops in every possible path. The algorithm then select the path with a minimum number of hops. All this information of a path, a packet will take in order to go from node i to j is described and summarized in the routing table, which is based on the reliable links of the network. The routing table for network B derived from the MHA is shown below in Table 2.2. Again, e.g., to get a packet from node 1 to node 10, we consult Table 2.2 where the position (i=1, j=10) is equal to 2 which means to go first from node 1 to node 2 or use first the link (1,2) and so as was outline above; rij indicates the one-hop sequence predetermined by the MHA in order to go from node i to node j.

The MHA uses static table-based routing where a node consults a table to select the outgoing link on which the packet is to be forwarded. This algorithm counts the number of hops in every possible paths and selects the path with a minimum number of hops. Actually, the MHA can be seen as a variation of the Maximum Forward Progress within Radius (MFR) algorithm [3,5]. In the MFR algorithm, a station transmits its packet to the station that is as close to the final destination as possible, limited only by the transmission range. MHA can be seen as a terrain adaptive MFR a strategy in the sense that the transverse distances in each hop are maximized. However, the MHA does not always choose its next node in the direction of the destination node. MHA is not a distributed algorithm since it uses knowledge of the entire network, whereas MFR is a completely distributed algorithm based on the local knowledge of each node but it needs to know the direction of the intended receiver.

22

Table 2.2 Routing table of the network B.

Another convenient description of the connectivity properties is the average hop count ( h ) which is defined as the average length of a ”shortest” path taken over all pairs of nodes. This parameter is calculated as follows:

hN N

ijjN

iN

=∑∑

−==1111 π

(2.25)

πij 1 2 3 4 5 6 7 8 9 10

1 --- 2 2 2 2 2 8 8 9 2

2 1 --- 3 4 3 4 3 1 9 3

3 2 2 --- 4 5 4 7 8 9 10

4 2 2 3 --- 5 6 7 3 2 10

5 3 3 3 4 --- 6 3 3 3 10

6 4 4 4 4 5 --- 4 4 4 10

7 8 3 3 4 3 4 --- 8 9 3

8 1 1 3 3 3 3 7 --- 1 3

9 1 2 3 2 3 2 7 1 --- 3

10 3 3 3 4 5 6 3 3 3 ---

where 1 i; j ≤ N , and stands for minimum number of hops separating nodes i and j i.e. the hop count achieved by the MHA. Alternatively, the routing matrix might be described as , where is the minimum number of hops from node i to node j.

≤ i ≠ j

}

π ij

π ij{π ijπ =

2.1.6 Traffic model

When discussing network performance, we should carefully specify the traffic model being used. Important parameters in our traffic model are the packet length, the arrival process, the queueing process, and the traffic matrix. As mentioned previously, packets, are assumed to be of constant length. Besides, packet arrivals are modeled to occur according to a Bernoulli process with mean over the network. Let us name λ as the total traffic load of the network. Furthermore, packet arrivals at a node are of two classes (1) external and (2) internal. External arrivals to node i are assumed are generated by an independent Bernoulli process with mean

λ

λ i = λ /N (packets per slot) i ∈[1,N] (2.26)

23

λλ

2 =N

1

2

3

4

λλ

1 =N

λλ

3 =N

λλ

4 =N

, Node # ....

λλ

5 =N

5

Legend: #

Figure 2.8 The traffic model for a network of five nodes (N=5) with uniform traffic.

and originate from some attached device(s) to node i, i.e., a computer or external source to the network. Figure 2.8 represents the traffic model used for a network of five nodes. Moreover, internal packets arrive from other nodes and can further be classified as: transit packets that must be retransmitted to others nodes after they are received, and terminal packets that are destined to the node and therefore need not be relayed. Each station is assumed to have a buffer of infinite size. Packet arrivals at a node will be illustrated in Figures 3.1 and 3.2. The queueing process for each one of the MAC protocols concerned will be briefly described in Chapters 3 and 4. We also relate the total traffic with the individual external arrivals a at each node as follows: λ λ= ∑

=i

i

N

1 (2.27)

The traffic matrix is defined as µ , where { }µ= ij µ ij is the expected number of packets per

slot generated at node i with final destination node j. We assume a uniform traffic matrix, i.e.:

µ

λ

ij

i

N=

−≠

1

0

i j

i = j (2.28)

24

Since the MAC protocols are designed to provide reliable links between nodes, the link traffics are of our interest. One way to estimate the amount of traffic on each link is presented in [15, 26]. The idea behind this is to take advantage of the uniform distribution assumption and obtain the number of paths that use a particular link (i,j). With this information, we can build a ”load matrix” which is a valuable tool to study traffic ”adaptive” multiple access protocols, i.e., a traffic-sensitive spatial TDMA algorithm allocates slots depending on the estimated amount of traffic passing through each link. Next, we explain this approach to estimate the load matrix. We can start by consider a fully connected network where the expected traffic in each link (i,j) per slot is the same, namely:

λ µλ

ij ij N N= =

−( )1 (2.29)

However, due to some links in the network are not usable (i.e., they are characterized by a too high loss), it is necessary to route their expected traffic through other reliable links. This produces uneven loaded links compared to the fully connected network. In this situation is convenient to re-formulated the right side of equation 2.29 to include the routed traffic. Moreover, since we have assumed that there are several and uniform packet streams µij packets/sec, each following a unique path that consists of sequence of radio links through the network. Then the total arrival rate at link (i,j) is [26]:

∑∑ == j)(i,link thecrossing ),( sin

pathij

jilinkthegcrosstreamspacketall

ijij µµλ (2.30)

Thus, we might consider the number of paths using a particular available link. Denote the number of paths that use the link (i,j) as , in a connected network. Thus, our load matrix is defined as P = { P

( )P ij

(ij) }, where P (ij) is also an undirected measure of the amount of traffic load that can be expected to transverse the link (i,j). We can see from (2.30):

( )λλ

ijij

N N hP=

−( )1 (2.31)

It should be noted that some = 0 when the link (i,j) is not usable or unreliable. λ ij

From Eqn. 2.30 we have: (2.32)

25

Table 2.3 Load matrix for network B under uniform traffic assumption.

Node 1 2 3 4 5 6 7 8 9 10

1 0 0 0 0 4 0 7 2 0 4

2 0 0 0 0 9 0 0 0 0 0

3 0 0 0 9 0 6 0 0 0 10

4 0 0 9 0 0 0 0 0 0 0

5 4 9 0 0 0 0 0 4 0 8

6 0 0 6 0 0 0 5 5 0 1

7 7 0 0 0 0 5 0 0 3 0

8 2 0 0 0 4 5 0 0 0 2

9 0 0 0 0 0 0 3 0 0 6

10 4 0 10 0 8 1 0 2 6 0

( )P

N N hij ij=−λ

λ( )1

(2.32)

Moreover, we introduce , the estimated amount of traffic passing through each node i as:

P i( )

( )P Pi ij

j

N i

= ∑=

( )

1

Moreover, to compute the load matrix we proceed as follows. As an example we consider network B which is depicted in Figure 2.7. To find a path between node 1 to node 3 an imaginary line is drawn between the two nodes. Next, we refer to the routing table, Table 2.2, where it is instructed to use the route or path 1-2-3. The amount of traffic on links (1,2) and (2,3) is then incremented by 1 unit, respectively. The same procedure is repeated for every route in the network. When routes between every distinct pair of nodes are taken into account, the matrix of the load on each link (in Table 2.3) can be generated. 2.2 Performance measure

The merging of computers and communications during the past two decades has led to an explosive growth in communication networks. Performance measures used to evaluate communication networks vary depending on the type of network being analyzed and the applications being used. For multihop PRN:s, the commonly used performance measures are throughput, and delay. Below, the throughput is defined:

26

Throughput is: The expected number of packets that reach their final destination per slot in the entire multihop network. It a measure of the degree of utilization of network resource. However, the main performance measure of interest is the average expected packet delay, D. Packet delay is defined as: the time between the arrival of a packet at the buffer of the originating station and the end of the slot in which is successfully received at the final destination station. In the described network of N nodes, in general, a randomly selected packet to be transmitted from node i to node j has the delay , expressed in timeslots. If two nodes are neighbors, one successful transmission will require one timeslot. However, due to the fact that is a random variable one must resort to make statistical interference of by means of this expected value

Dij

Dij

Dij

(2.34)

where , D ,..., be a sample of the random variable from a single simulation run (Section 2.3) and n is the number of packets successfully received in that run between node i and j.

Dij( )1

ij( )2 Dij

np( ) Dij

p

E D ED

nij

ijk

k

np

p

[ ]

( )

=

=∑

1

The average expected delay to transmit a packet from node i to j, can be formulated as,

[DN

E Diji j

N

j

N

=

= +=∑∑1

211

] (2.35)

where E[ ] is expressed in expected delay between node i and j. Dij

Furthermore, if we let E[ D Hij λ, ]

λ

be the expected delay to transmit a packet from node i to j given a certain traffic load and some given terrain H, the average expected delay in this case can be expressed as,

[D HN

E D Hiji j

N

j

N

( , ) ,λ =

= +=∑∑1

211

]λ (2.36)

Optimum network performance is achieved in our context when the D( ,H) is minimized by one parameter of the MAC protocol.

λ

27

Unstable System: is one where the expected number of messages in the system grows without bounds. So, in, in this state the PRN is not very useful due to D will be very high. Our criterion for instability is the queue length at each station. If any of the queues at any time exceeds than 20 packets, we consider the system to be unstable. It should be noted that stability is not the main focus of this thesis. 2.3 Performance Evaluation

An exact analysis for the average expected delay using queueing analysis in multihop PRN:s has not been carried out for Eqn. 2.36, it is very difficult [12] due to the queueing dependency among the nodes and the large state vectors involved. For these reasons, we have chosen computer simulations as our performance evaluation method. In simulations of this kind, various components of the actual PRN (network topology, antennas, radio links, queues, multiple access protocols, network control structures) are represented in a computer program. The events that would occur during the actual operation of the network (arrivals, transmissions, routing and departures of packets, error conditions such as packet loss due to noise and radio interference) are generated during the execution of the program. In general, the simulation program generates events and then simulate the network's response based on these events. The simulation program also gathers data during the simulation and computes performance measures. The performance evaluation is described in appendix A, where tables of simulation parameters are shown. Before we present the models used, let us introduce a typical scenario for our study: We start by consider an area without telecommunication infrastructure, where in part of it is required to provide data communications, e.g. in a rural environment. We assume that the terrain area under study contains mountains and valleys, but the vegetation is not considered. We use N-nodes PRN:s, which will be deployed in the terrain of interest in order to support data communication. These nodes are equipped with omnidirectional antennas, and they can transmit using relative low power level. A node must be in either the transmitting mode or the receiving mode, and not both. To achieve reliable communication beyond the radio range of the individual nodes multihop transmission technique is used. In addition to that, the nodes can handle data rates of Kbits/s, and they use a binary modulation scheme combined with a simple error coding which allow them to have a bit error rate . Indeed a node transmitting a packets is advised of the correct reception by an acknowledgment packet.

Rb

Pε

The results in this thesis has been obtained under the following assumptions:

28

• = 100 Kbits/s (symbol duration is long compared to spread delay, since in most

outdoor areas the rms multipath spread measured at distance up to a few kilometers is < 10 [42]).

Rb

µs• . Pε ≤ 10 6−

• Packet length : 5 bytes header + 35 bytes information. • The time axis is divided into timeslots, each the length corresponding to the

transmission time of a packet. All packets are assumed to be of the same length. The propagation time is ignored.

• The operating frequency of the network is 300 MHz. • Terrain profile and obstacles in the path between two nodes according to the terrain

model in section 2.1.2. • All nodes are assumed to be equipped with an omnidirectional antenna transmitting at

the same power . Transmitter power, : -5 dBW ( mW). Pt Pt Pt ≈ 316

29

r• Antenna gains ( ) : 3 dB. The antenna height at a node: 20 m above the ground. G Gt ,

• We assume a simple model, where if the Signal-to-Interference-Ratio (SIR) is above 10 dB and the given , the acknowledgment traffic can be then neglected. Pε

Chapter 3 Slotted ALOHA Given the matrix gain derived from the terrain model, a sample network and a simple routing policy (MHA) described in the previous Chapter, we can now examine the multihop Slotted ALOHA (S-ALOHA) protocol in the given terrain. In this Chapter, we investigate the effects of various factors (e.g., traffic load) on the network performance. In Section 3.1, we begin by describing S-ALOHA. We study the influence of the traffic load and the network connectivity on the average expected packet delay. In sections 3.2 and 3.3, two strategies will be examined with respect to a key parameter of the MAC protocol. Finally, from the studies mentioned above, we will propose a new assignment that ”nearly” minimizes the network delay. 3.1 S-ALOHA protocols in multihop environment Slotted ALOHA [2-5] is a random access protocol, where nodes are allowed to transmit packets only at the start of a time slot. We assume that a node (Figure 3.1) will try to transmit whenever it holds a packet in its queue, and that the node transmits a packet according to a Bernoulli process with parameter q in a slot. The term q goes under the name transmitting probability. Since there is no coordination among the nodes, collision (overlapping in time at the receiver of packets sent by two or more different nodes) can occur. However, when two or more packets arrive at the receiver at the same time, either a collision occurs (i.e. no packet can be successfully detected) or the strongest packet, (i.e. the packet with largest received power) can survive if the SIR is above a SIR target. Nodes can detect collisions by various mechanisms, e.g., a node transmitting a packet is advised of the correct reception by explicit acknowledgment message sent by the receiving node. If the transmitter does not receive this acknowledgment after an appropriate interval, it presumes that a collision has taken place. Here, the time that a node takes to receive an acknowledgment is neglected, such that each node is assumed to know immediately after it transmitted its packet if the reception was successful or not. Once the transmitting station detects a collision, it retransmits the packet after a random amount of time and continues to do so until the packet has been successfully received. Conversely, when the node receives an acknowledgment the packet under transmission is removed from the queue.

Chapter 3. Slotted ALOHA

Terminal

packets q

ALOHA

TransmitterRouter

External packets

Queue

Receiver

FCFS

Antenna

Internal

packets

Transit

packets

λi

Figure 3.1 A packet radio node in multihop slotted ALOHA. A packet radio node consists of a receiver, a router, a queue (buffer) and a transmitter (Figure 3.1). At any slot, a node i can be in one of two states: active (when there is a non-empty buffer) or idle (when the buffer is empty). An active node is either in transmitting mode with probability q or in receiving mode, with probability 1-q, where 0 < q 1. Packets are serviced on a First Come First Serve (FCFS) basis.

≤

We are also reminded that the single-hop S-ALOHA can be considered as a fully connected network. This can be considered to be equivalent to the case where all nodes transmit packets over a common broadcast radio channel to a central receiver [8]. If a packet is successfully receive at the central node an acknowledgment is sent to the transmitting node. On the other hand, in a multihop S-ALOHA system, nodes are allowed to transmit to each other directly, i.e. there is no central receiver which ”repeats” packet to the intended node. However, the multihop topology adds another possibility for packet collisions. This might occur when a node transmits to another node which is also transmitting in the same slot. S-ALOHA for multihop networks can be seen a generalization of S-ALOHA for single-hop networks. Unless otherwise stated here, the term S-ALOHA refer to the multihop S-ALOHA. Some of the studies of S-ALOHA protocols have been done by using the heavy load approximation [3,5-6]. This means that all nodes are assumed to always have packets to transmit. The delay of a prioritized packet that will always be placed at the head of the buffer is studied, such a packet will not experience any queueing delay. In this context, we overestimate the interference whereas, estimates of the queueing delay are clearly optimistic since the ”best” packet experiences no such delay. In contract to this, we will in our study consider also the queueing delay in the network performance.

32


In the multihop S-ALOHA scenario, we study the effect of various factors: the transmission probability q, the capture threshold , the total traffic load and the terrain for different values of the height parameter ( ); on the average expected delay (D). In particular we will be interested in finding The optimum transmission probability q* : which is the q that minimizes the average expected packet delay defined in the previous Chapter.

γ o

σ

λ

Thus, we examine the average expected delay, D versus λ for different values of q. D versus q for various values of . We assume a given constant threshold value, e.g., = 10 dB for both situations. Later, we will examine D as a function of the traffic load ( ) for various values of . Finally, the D in terms of the capture ratio (in dB) will be addressed.

λ γ o

λσ

3.1.1 Numerical Results In this section we will numerically evaluate the performance of S-ALOHA networks in rough terrain. Throughout the study we will use some sample networks, denoted A, B, C and D (Appendix D). Network B has the higher connectivity ( N = 4.2 nodes) whereas network D has the lowest connectivity ( N = 3 nodes). The basic set-up of parameters of the simulated environment is outlined in Table 3.1. Details of the simulation are found in Appendix A.

Number of nodes 10 Threshold path loss 130 dB SIR threshold 10 dB γ o

Frequency 300 MHz Number of simulated arrival events 10.000

Table 3.1 Basic simulation parameters. The influence of the transmission probability (q) on the performance is examined in networks A and B. In Figures 3.2 and 3.3, the delay as a function of is shown for several values of q, when N=10 nodes. However, due to the capture effect, the queueing

λ

modeling and the terrain shadowing, it is possible to use higher transmission probabilities for S-ALOHA than those given in the literature [5-6,18] derived for fully connected networks. This could mainly be attributed to the fact that due to the capture

33


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts

λ in packets\slot

ab

cd

Figure 3.2 (Network A). Average expected delay (in timeslots) as a function of (traffic

load), with q as a parameter. The capture parameter: = 10 dB.

λγ o

a) q = 0.5, b) q = 0.4, c) q = 0.3, and d) q = 0.2.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts

a b cd

λ in packets\slot

Figure 3.3 (Network B). Average expected delay vs. , with q as a parameter. The

capture ratio is: = 10 dB. λ

γ oa) q = 0.5, b) q = 0.4, c) q = 0.3, d) q = 0.2.

34


phenomenon, some transmissions are successful even if there are "colliding" packets. In fact, it should be noted that the real q* varies with the total traffic load and the network connectivity, that suggest an optimum performance envelope for the network. In general, the network delay is influenced by the connectivity. In our sample networks (Figures 3.2 and 3.3), increasing the number neighbors by choosing, for instance, the network topology improves the probability of being able to make a connection while decreasing the number of hops required. Conversely, a larger number of neighbors may lead to higher probability of packet collision. Thus, a network with higher connectivity may restrict us to lower transmitting probabilities in order to keep S-ALOHA out of the region where the queues grow very quickly. In the former numerical evaluations, and in the rest of the thesis, we neglected the noise power when interference is present at the receiver site. This does not seem to affect our results significantly as it can be seen in Fig. B.1, Appendix B, where we have similar calculations as in Fig. 3.3 where we have included the noise power. In Figure 3.4, the delay as a function of q is shown for different values of (network A). To simplify the analysis, the heavy load approximation is often used. Previous results using this approach stated q* to be 0.14 for 20 nodes [18]. In Figure 3.4 (curve a) the heavy load approximation is illustrated, disregarding the queueing delay, q* decreases to 0.13 for 10 nodes. As we can also observe in Figure 3.4, the heavy load approximation is a very pessimistic assumption for low traffic conditions, e.g., = 0.1. On the other hand, this approximation is too optimistic for high load conditions, e.g., =0.4. This is explained by the fact that under the heavy traffic approximation, where a "suitable" packet are ready for transmission at all times, the queue delay is neglected whereas in our analysis it is taken into account. For the continuos curves in Fig. 3.4, it is important to notice that the network delay has for each traffic load a minimum, which suggests a way to find q*. This ”convex” behavior of the network delay might help us to assign transmission probabilities in the multihop S-ALOHA, later. We will elaborate more about this in Section 3.2.

λ

λ

λ

35


10−1

100

101

102

q

D in

tim

eslo

ts

a

b

c

d

e

Figure 3.4 (Network A). Average expected delay versus q (transmission probability), with

as a parameter. The capture ratio is: = 10 dB. λ γ oa) under the heavy load approximation (- - -).

Under different traffic loads b) = 0.4, c) λ = 0.3, d) = 0.2, e) =0.1. λ λ λ

Further, we study the influence terrain topology on the network behavior. Here, we study the effect of varying the height parameter ( ) as illustrated in Figure 3.5 (network A). We see that a terrain with terrain roughness (with mountains) in comparison with a flat terrain ( σ ≈ 0) , e.g. regarding the same PRN, the former one will yield higher path losses due to the diffraction losses of the hilly terrain. In this manner, we can study the influence of the terrain for a particular transmission probability, e.g., q = 0.30 by changing only the roughness of it. Under the condition the network remains connected, a rougher terrain will in general cause a higher propagation loss which has a "negative" influence on the network connectivity.

σ

N tends to decrease as is increased. Furthermore, the delay as a function of the total traffic for several height parameters with the same terrain is shown in Figures 3.6 and 3.7.

σ

When the shadowing (diffraction) losses can be neglected, i.e. 0, it can easily be seen in Figures 3.6 and 3.7 that network delay improves compared to the rougher terrain only for the low traffic loads ( λ < 0.3). The delay performance then decreases with smaller as a result of the low possibility of collision due to the low traffic situation and the fact that packets will have fewer expected hops compared to a situation with higher σ . Therefore, for low traffic loads a rougher terrain will cause a higher network delay.

σ ≈

σ

36


0 20 40 60 80 100 1202

3

4

5

6

7

8

height parameter in m

Ave

rage

# o

f nei

ghbo

urs

Figure 3.5 Network A with ρ = 3 m. Connectivity ( N ) vs. the terrain height parameter ( ). σ

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts

λ in packets/slot

a

b,c

b,c

d

e

Figure 3.6 (Network A). Average expected delay as a function of . Transmission probability q = 0.30 is considered.

λ

For different heights a) σ = 100 m ( N = 2.8 nodes), b, c) = 40 m, 80 m (σ N =3.2 nodes),

d) = 20 m (σ N = 4.8 nodes), e) 0 (σ ≈ N = 7.6 nodes). All the former cases used ρ = 3 m.

37


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

D in

tim

esl

ot

a

b,c

c

d

e

f

b

λ in packets\slot Figure 3.7 (Network B). Average expected delay vs. . With q = 0.30. λFor different heights a) σ = 100 m ( N = 2.6 nodes), b, c) σ = 80 m ( N = 3.0 nodes), 60 m

( N = 3.4 nodes), d) = 40 m (σ N = 4.2 nodes), e) = 20 m (σ N = 5.8 nod.), f) 0 (σ ≈ N = 7.6 nodes). All the former cases used ρ = 3 m.

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts

λ packets\slot

a,b,c d e

Figure 3.8 (Network A) Average expected delay vs. for various :s. q = 0.30. λ γ o

a, b, c) = 15, 12,10 dB (γ o N = 3.2 nodes)

d) = 7 dB (γ o N = 4 nodes)

e) = 5 dB (γ o N = 4.2 nodes).

38


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts a

b

c d e

λ in packets\slot

Figure 3.9 (Network B) Average expected delay vs. for different :s. q =0.30. λ γ o

a) = 15 dB (γ o N = 3 nodes)

b) = 12 dB (.....),γ o N = 3.4 nodes

c) = 10 dB (γ o N = 4.2 nodes)

d) = 7 dB (γ o N = 5.6 nodes)

e) = 4 dB (γ o N = 5.6 nodes).

On the other hand, for 0.3 , intermediate values ( ) of the height parameter σ produce connectivities that are favorable to the network delay. Therefore, we can handle higher loads in comparison with the flat terrain. The reason for this is the trade-off between having a larger number of intermediate hops and a lower network connectivity having fewer collisions. Finally, a rougher terrain, e.g., σ = 100 m leads to an adverse situation where the expected number of hops increases even though the interference is minimal due to a lower number of neighbors as a consequence of the shielding provided by the mountains in the terrain.

≤ <λ 0.4 40 80m ≤ ≤σ m

The network delay in terms of the total traffic for various SIR threshold values (in dB) is shown in Figures 3.8 and 3.9. Of course, for lower values of , the capture effect is accentuated and there are fewer collisions causing the network delay to decrease. On the other hand, for higher values of , we will have more collisions, and the average expected delay increases then. Note that curves a, b and c (Fig. 3.8) have the same network delay characteristics since they produce a similar connectivity. However, in our networks, also affects the connectivity. For instance, in Fig. 3.9 ( = 15, 12, 10 dB), at high traffic loads higher connectivity will cause more collisions even if we have a lower value of which increases the network delay.

γ o

γ o

γ o

o

γ o

γ

39


In summary, we have examined the multihop S-ALOHA protocol for varying traffic load, several transmission probabilities, different threshold parameters and various terrain height parameters. Our analysis shows that it is necessary to have a some sort of control over the influential factors for this protocol to operate stable. Imagine that we have a three variables ( q o, ,γ N ) to tune the MAC protocol, S-ALOHA, in order to achieve an ”optimal” network behavior. In particular, to study the impact of the connectivity is very attractive since we can control it by means of other factors, most of the time available to the designer, as: the transmitter power, the antenna type and orientation, the antenna height, the distance separating two nodes (not considered here), etc. In our sample networks, we have observed that if the traffic load is increased or if connectivity is increased, we must decrease the transmitting probability to remain in the lowest part of the average expected delay curve (Figure 3.4). In general, rougher terrain constrains the network delay performance for traffic loads ( λ < ). Therefore, if we take a rather broad perspective on what has been analyzed it may be worth-while studying the selection strategies of the parameter q as a function of the connectivity and/or the total traffic load when the network delay is minimized or favorable. This objective is the subject of the next two sections.

0 3.

3.2 S-ALOHA with constant transmission probability policy In the design of a S-ALOHA network, it is valuable to find a simplified way of choosing a proper value of q. In seeking a coherent policy for assigning transmission probabilities with this protocol, we investigate a few possible candidates. A straightforward procedure that comes to ones mind is to utilize the inverse of the average number of neighbors ( N ) in a network as a "good guess" value for q. For instance, using this simple assignment policy would yield q 0.31 for the network A, which is close to q* = 0.39 derived from Figure 3.4 (for =0.3). We will now investigate whether it is possible to "generalize" this simple assignment policy assuming each node uses the same q. However, in order to evaluate network delay, we first generate random networks of N uniformly distributed nodes on the irregular terrain. Secondly, for each of these networks, the average expected delay and

≈λ

N is computed for different traffic loads, . Next, we numerically estimate the optimal q. This is done by taking the value of q that corresponds to the minimal value of the estimated average expected delay in each network.

λ

Using 50 random networks for =0.3 with the policy q C/λ ≈ N where is C is a constant we obtain the results shown in Figure 3.10. In fact, the policy mentioned above, q = 1/ N , corresponds to the case C = 1 (curve c) which unfortunately seems to give a rather poor estimates of the q*, and a better approximation is shown by curve a (C=2). So far, only the

40


connectivity issue of the network has been address. Moreover, we might refine our analysis if we also include the traffic load. Thus, Figure 3.11 shows the results for 25 different random networks under several traffic loads ( ), and notice that the stars represent the gathered data from the experiments. We investigate the following candidate strategies to estimate q* :

λ ≤ 0.4

q I

6

Strategy I : = - q I c1 c2 λ N where 0.72 and c 0.23 (3.1) c1 = 2 =

Strategy II : = 0.75 = 0.75 (0.72- 0.23qII q I λ N ) (3.2) Strategy III: =C / qIII λ N where C= 0.4 (3.3) In Figure 3.11.a, the Strategy I is a linear approximation to the real data (q*). For instance, in network A, q* = 0.39 , for = 0.3, whereas (3.1) gives = 0.49 for the same traffic load. Furthermore, if we take a look at the queue length situation (Fig. B.2, Appendix B), we can observe that the queues grow up very rapidly around a q = 0.45 and afterwards. Subsequently, in order to compensate for the dispersion of the real data due to the fact that

λ

N (Eqn. 3.1) cannot refer to only one particular network, and the

1 2 3 4 5

7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mean # of neighbors

q*

a

b

c

Figure 3.10 Optimal transmission probability (q*) vs. connectivity for =10 dB, and

= 0.3. MAC protocol: S-ALOHA with constant q. Terrain parameters are: = 40 m &

γ oλ σ ρ = 3

m. Experiments of 50 random networks and N=10 nodes. a) (___) q =2/ N , b) (*) gathered q*

from the experiments, c) (---) q =1/ N .

41


0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

q*

I

II

λ x mean # of neighboursa.

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

q*

x mean # of neighboursλb.

III

Figure 3.11 Optimal transmission probability (q*) as a function of λ N for = 10 dB

and . MAC protocol: S-ALOHA with constant q. Terrain parameters are: = 40 m &

γ oλ ≤ 0.4 σ ρ =

3 m. Experiments of 25 random networks and N=10 nodes. a. Strategy I and Strategy II for

q*. c. Strategy III to the q*.

instability previously mentioned; we apply a correcting factor (i.e., 0.75) to the former in (3.1). This results in the Strategy II (Figure 3.11.a).

q I

In the lower plot (Figure 3.11.b) we attempt to approximate the collected data by the Strategy III (the dotted curve). In Figure 3.11, we can observe that this first approximation (Strategy I) gives a rather good idea of how to choose the transmission probability q* for a particular network. However, the results for this approximation, yield very optimistic q* since we are close to the unstable region of the network delay curve. This leads us to the second Strategy. In our sample networks, the Strategy II has shown to work better than q ≈ −N 1 , as well as Strategy I and III. Certainly, the Strategy II is a little more conservative than Strategy I;

in Eqn. 3.2 will be used for further studies. We will in the following refer to Strategy II as the CONSTQ approach. q II

42


3.3 S-ALOHA for node adaptive transmission probability policy

So far, we have studied the case of the assignment policy under constant transmission probability. Now, we turn our attention to another type of transmission probability assignment, namely where the transmission probability for each node can be different. This approach seems interesting since some studies [35] suggest that throughput optimization for the multihop slotted ALOHA is achieved by an adaptive node transmission probability assignment policy. Our first heuristic strategy could be to assign the transmitting probability for node i as, q , where is the number of neighbors of node i. One special case is =1, where we assign = 1/2 as shown in Table 3.2 for network A. The results of the average expected delay are obtained by means of simulation for this policy and they are shown in Figures 3.12, 3.13 and 3.14 (the dash curves). We name this approach VARQ1, (see Eqn. 3.4).

i = 1 / N i N i

N i q i

q i = 1 / N i (3.4)

i 1 2 3 4 5 6 7 8 9 10

4 1 3 1 4 4 3 4 2 6

q i 0.25 0.5 0.33 0.5 0.25 0.25 0.33 0.25 0.5 0.17

N i

Table 3.2 (Network A). Transmission probability assignment for the approach VARQ1.

In our sample networks, VARQ1 however performs poorly in comparison with the CONSTQ approach as illustrated in Figures 3.12, 3.13 and 3.14. This is because VARQ1 does not take into account the traffic load situation. Moreover, we can weight each node transmitting probability using the information of the load matrix introduced in Chapter 2. In other words, we add the impact of the load matrix in the selection of the node transmitting probabilities, assuming that q is proportional to the estimated traffic that passes through each node. This node traffic estimate can be computed by using the traffic matrix and the routing algorithm and we call this approach VARQ2. The second heuristic expression for the individual transmitting probability of node i can be expressed as:

i

(3.5) qi f

NPP

qi

i

= ⋅ ( )

where

43


PP

N

i

i

N

= =∑ ( )

1 (3.6)

and the ratio P i( ) /

fq

P gives an estimate of the normalized amount of traffic passing through node i. In (3.5) we have introduced the factor , which may ”adjust” the node transmission probability to the traffic load variation. Further, Table 2.3 illustrates the load matrix for network B. Table 3.3 shows the transmission probability assignment VARQ2 makes for network B under conditions expressed in Table 2.3 for =1. Results with some values of for three sample networks, namely, Network A, B and C (refer to Appendix D) are also shown in Figures 3.12, 3.13 and 3.14, respectively.

fq

fq

In Figure 3.12, we study the network A under this last transmission assignment policy. Fig. 3.12.a illustrates VARQ2 with =1.75. Looking more closely at the delay characteristics of this curve, we see that for a range of the traffic loads between 0.05 and 0.17 the VARQ2 marginally outperforms the CONSTQ approach. Also, Figure 3.12.b also shows a similar performance for the case VARQ2 with =1.5, but for a slight different traffic load range. In Figure 3.13.a, we show the average expected delay versus the total traffic load in network B, for VARQ2 where we have various values of . VARQ2 shows modest improvement in comparison of the constant transmission probability approach (curve c). Finally, in Figure 3.14, VARQ1 with =1 (curve c) shows higher throughput at high traffic load than CONSTQ approach (curve b).

fq

fq

fq

f q

node # P i( ) N i qi

1 13 3 0.29

2 23 4 0.39

3 35 7 0.34

4 21 6 0.23

5 9 4 0.15

6 9 3 0.20

7 9 4 0.15

8 11 3 0.25

9 9 4 0.15

10 9 4 0.15 P 14.8

Table 3.3 (Network B). Transmission probability assignment

for the approach VARQ2 with = 1. fq

44


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts

a b c d

λ in packets/slot

Figure 3.12 (Network A). Average expected delay vs. for = 10 dB. MAC protocol: λ γ oS-ALOHA with node adaptive q.

a) (____) VARQ2 with =1.75, b) (____) VARQ2 with =1.5 fq fqc) (- - -) VARQ1, d) (.....) CONSTQ .

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts

λ in packets/slot

a bc d e

Figure 3.13 (Network B). Average expected delay vs. for =10 dB. MAC protocol: λ γ oS-ALOHA with node adaptive q. a) (- - -) VARQ1, b) (.....) CONSTQ

c) (____) VARQ2 with = 1.90, d) (____) VARQ2 with = 1.75 fq fq

e) (____) VARQ2 with = 1.50 fq

45


46

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

D in

tim

eslo

ts

λ in packets/slot

a

b

c

Figure 3.14 (Network C). Average expected delay vs. for =10 dB. MAC protocol: λ γ oS-ALOHA with node adaptive q. a) (- - -) VARQ1

b) (_____) VARQ2 with =1 fqc) (.....) CONSTQ .

In summary, in Figures 3.12, 3.13 and 3.14, the network delay is depicted for the CONSTQ, VARQ1 and VARQ2 assignment policies. We can see that the VARQ1 performance is inferior to the other approaches. Generally speaking, the VARQ2 strategy exhibits slightly better performance than CONSTQ. This is probably due to the fact the VARQ2 (with the right ) is more adaptive to the traffic load situation in comparison with CONSTQ. From the latter Figures, it can be seen that we do not gain much by using the node adaptive transmission probability approach VARQ1. Thus, in our sample networks, we have achieved better network performance with the transmission probability assignment, CONSTQ. With VARQ2 we have explored other alternative approach, which needs further refining as our results exhibit. Moreover, the approach CONSTQ has been obtained in a more general basis, there is a specific procedure to calculate q*, and it is more robust then. Conversely, the VARQ2 scheme is just a simple transmission probability assignment, which has not been ”optimized”. Of course, an optimal adaptive transmission probability policy should always be better than CONSTQ.

fq

Chapter 4

Spatial TDMA

In order to avoid collisions, deterministic transmission schedules such as Spatial TDMA

(S-TDMA)[12] have been proposed. In these schemes, transmission schedules are

coordinated in such a way that no conflicts occur. S-TDMA defines a repeating

transmission schedule (frame) which contains a fixed number of slots, with each slot

being assigned to a unique set of non-conflicting links. This Chapter considers link

allocation schedules, when the network gain matrix and some information about the

load matrix are taken into account. When we incorporate the load matrix to make the

transmission schedules, we say that we have a traffic-sensitive S-TDMA. Section 4.1

introduces the basic technique to create the S-TDMA frame in the multihop

environment. In Section 4.2, we examine the non-sensitive traffic schedules, whereas

Section 4.3 investigates the traffic sensitive S-TDMA. Finally, comparisons between S-

TDMA and the S-ALOHA channel access protocols are made in Section 4.4.

4.1 Spatial TDMA in multihop scenarios

S-TDMA for multihop packet radio networks is a generalization of TDMA for single-

hop networks. Its aim is to provide a conflict-free transmission schedule that gives each

link at least one slot. In order to better explain how S-TDMA works, we need a set of

proper terms. The terms we will use are: arc, clique, and schedule [12,30].

Arc: It is just a link. It represents one-way radio communication between

two nodes. The arc is the basic cell of the S-TDMA protocol.

Arc is a natural way to link the network’s connectivity diagram with the procedure to

create the S-TDMA schedule. Also, in the literature an arc is commonly called a

directed arc.

Clique: A set of arcs that can carry packets simultaneously with no

collision at the receiving nodes of these arcs.

That is, a clique allows all its member arcs to simultaneously transmit successfully. A

maximal clique is one in which no additional arcs can be added.

Chapter 4. Spatial TDMA

Figure 4.1 A packet radio node in multihop spatial TDMA.

Schedule is: a set of maximal cliques which contains all arcs in the radio network.

Each frame of the protocol consists of a number of slots that are allocated to a set of

conflict-free transmissions in the network. That is, S-TDMA defines a repeating frame

which contains a fixed number of slots, with each slot being assigned to a unique clique

in the schedule. Note that we use synonymously the words: schedule (radio network

studies) and frame (common term in the conflict-free access protocols).

In general, from the path loss and connectivity models is possible to determine in which

combination arcs can be used simultaneously without conflicts. The compatibility

between arc i and arc j is represented by the element cm ij( ) in the so-called

Compatibility Matrix (CM), which is defined as [12]:

cm ij( ) =1

0

if arc i and arc j can be used in the same slot without collisions

if arc i and arc j can not be enable simultaneously in the same slot

(4.1)

When a transmission takes place over an arc of the network, we say that arc is activated

or enabled. We also define the scheduling delay as the time in slots that it takes the

same arc to be activated again. A model describing a packet radio node in S-TDMA is

shown in Figure 4.1. In this case, traffic arriving at a given node can be separated into

classes, where there is a class for each possible neighboring node to which the given

node can transmit. Here a priority queueing discipline is used where in every slot, the

transmitting node transmits the first packet destined to the scheduled receiving node, i.e.

it does not matter if this packet resides at the head of the queue or not.

Router S-TDMA Transmitter

schedule

Receiver

Internalpackets

Transitpackets Queue

TerminalpacketsExternal

packetsλ i

Antenna


1 2 3 4a.

1 2

4 32 3 23

2 1

3 4

1 2

4 3 ....

Slot 1 Slot 2 Slot 3 Slot 4 Slot 5 ....b.

time

Frame duration

Figure 4.2 Basic terms used in S-TDMA a. A tandem network of four nodes. b. Scheduleof the tandem network.

Figure 4.2 also introduces concepts, terms and notation used in S-TDMA. First, a

tandem network of four nodes is depicted in Figure 4.2.a. Next, in this network there are

six possible arcs (e.g., 1->2 which represents a unidirectional transmission from node 1

to node 2). In this example, we assume that the transmission range from a node is just

enough to ”reach” each one of its one-hop neighbors. In general, S-TDMA defines a

period of arcs transmissions, called schedule, in such a way that not conflicts occur.

Figure 4.2.b illustrates the schedule for the given tandem network. The frame duration,

expressed in slots, will be termed Fd (Figure 4.2.b). In this case Fd = 4 slots, so in the

slot number five the same cycle starts once more. If an arbitrary number is assigned to

the arcs in Figure 4.2, we might represent them as:

arc 1: 1-->2; arc 2: 2-->3; arc 3: 3-->4; arc 4: 4-->3; arc 5: 3-->2; arc 6: 2-->1

Figure 4.3 shows the compatibility matrix for the tandem network under study.

Figure 4.3 Compatibility matrix of the tandem network in Figure 4.2.

One maximal set of compatible arcs or ”maximal clique” consists of the positions (i,j) =

1 in the rows of the compatibility matrix. Unless otherwise stated, we use the word

CM =

1 0 0 1 0 0

0 1 0 0 0 0

0 0 1 0 0 1

1 0 0 1 0 0

0 0 0 0 1 0

0 0 1 0 0 1


clique to mean a maximal clique. For example, clique #1 corresponds to the ones in the

first row of the former compatibility matrix (Fig. 4.3)

clique #1 = { }arc 1, arc 4

which means arcs 1 and 4 are compatible or they can transmit in the same slot, e.g., in

slot 1 without conflict in Figure 4.2. Further, for the clique #2 we go down in the row 2

of the given CM and so on. In Figure 4.3, the clique #1 is equal to clique #4, and clique

#3 = clique #6.

We denote by Sx the schedule of network x. The schedule of the tandem network,

S tan dem corresponding to Figure 4.2.b is:

S tan dem = { } #2, clique #5, clique #3 clique clique# ,1

or in terms of arcs

S tan dem = { }arc 1 & arc 4 arc 2, arc 5, arc 3 & arc 6,

When designing S-TDMA algorithms, scheduling delays of arcs should be made as

small as possible. This could be achieved by minimizing the cycle length of transmission

schedule. Thus, in the classical approach, the objective is to find a link-activation

schedule of ”minimum-length” that satisfies the specified communication requirements.

However, the problem of determining the best schedule is a combinatorial optimization

problem of great complexity [34]. Because of this, heuristics are generally used to

produce suboptimal link-activation schedules. We discuss that the minimal network

delay in this MAC protocol is not only coupled to the length of the schedule, but the

routing algorithm as well. This may imply, that it is not certain that the minimum-length

schedule leads to the minimum average expected delay.

4.1.1 A Method of creating the S-TDMA Schedule

Let us first outline a brief description of the methodology used to create the schedule for

this protocol. We make use of an auxiliary flow diagram show in Figure 4.4. To do this,

we propose the following procedure based on [12,28,36]:

1) From the terrain model and the location of the nodes we calculate a gain matrix. By

using the MHA (routing algorithm) [18], we compute the routing matrix.


Start

Calculate Gain matrix & Routing matrix

Build the directed connectivity graph

Calculate the Compatibility matrix

Create the Basic Schedule (BS)

S-TDMA scheduletraffic-sensitive

Is this a

Compute the load matrix

Make Experiments

End

YES

NO

?

Detect the heavy loaded arcs

Assign extra slots to the former arcs in the BS

Figure 4.4 Flow diagram for creating the schedules in S-TDMA.


2) From the connectivity diagram (Figure 2.6), we generate a directed connectivity

graph, where each arc represents a unidirectional connection between a pair of nodes.

Figure C1 of Appendix C shows the directed graph for network A.

3) The CM is calculated by using the gain matrix of the network, the minimum SIR and

by employing Eqn. 2.21. In fact, this matrix is symmetrically binary (m x m), where m

is the number of arcs in the directed graph (in network A, m = 32).

In order to create the CM, we assign sequentially to each arc one row of the CM.

Suppose we start activating arc i, in this case in the row i. We then consider the

admission of the remaining arcs in crescent order (1,2,..j,...m), avoiding those arcs

where the transmitting and receiving nodes of arc i are involved. When an arc j, which

consists of node k and l, is a candidate to be activated in row i, we set Xk = 1 (Eqn.

2.21) for node k, which is supposed to transmit if arc j would be enabled. Further, we

use the Formula 2.21 to compute the SIR at the receiving node of arc i. We also

compute the SIR at node l of arc j. Finally, if these both SIR:s ≥ γ o the arc j will then

be activated. However, our calculations are not only made pairwise, but all previous

enabled arcs are considered when admitting a new arc. Indeed, our approach take

advantage of the gain matrix information. In summary, in such a matrix an 1 in the (i, j)

position indicates that the arcs i and j can be simultaneously enabled without a packet

loss at either of their respective destinations in the network. The CM is illustrated in

Figure C2 of Appendix C for network A.

4) As illustrated earlier, using the CM [12], one can generate a set of cliques,

containing arcs that can be enabled at the same time. If we let Ci denote the ith clique,

we can form a schedule, S, which is a set of maximal cliques { }S C C Ch= 1 , ,... , , where

each arc of the network is included in at least one member of S. Note that one possible

schedule is the set of all maximal cliques (h = m). In other words, for network A, the

coarse version of the schedule might be

where, for instance, the clique C1 consists of the following arcs,

{ }C1 1 6 16= , , ,20

S CA ii

=

=

∑1

32


In this clique we can enable transmissions for the arcs 1, 6, 16 and 20 in the same slot

without causing collision. In Figure C1 (Appendix C), the arc 1 corresponds to an

unidirectional link from node 1 to node 5 and so on. C1 is obtained by taking into

account the enabled arcs in row 1 (all the positions where we have 1) in the CM show in

Figure C2, Appendix C. A more detailed description of the set of all maximal cliques in

terms of the arcs is given in Table TC1 of Appendix C. We note that the duration of this

schedule will be 32 slots, one slot for each clique.

5) In general, using the set of all maximal cliques can lead to a new transmission

schedule. The ”old” one is the set of all maximal cliques. We try to find a schedule that

requires the fewest number of slots. To do so, we proceed based on the arcs contained in

the cliques by considering two cases: 1) the "untouchable" cliques that cannot be

excluded from the schedule (otherwise we would miss at least one arc) and 2) the

remaining cliques that are contained in unions of the untouchable cliques or not. For

instance, C6 is subset of C1 and C15 is covered between C18 and C21 .

In the follows we give an example of our methodology. First, from the coarse schedule

in 4), we start with a skeleton schedule by using the "untouchable" cliques (Table TC2

in Appendix C). We then count the arcs covered by the skeleton TDMA schedule to see

which arcs have not been considered yet (Table TC3 in Appendix C).

Finally, we add the necessary remaining cliques to the skeleton schedule to fulfill the

requirements of having at least one slot for each arc. Proceeding in this manner, we end

up with the following basic schedule for network A:

{ }S C C C C C C C C C C C C C C C C C C C C CA = 3 4 7 8 10 12 13 14 16 17 18 21 22 24 26 27 28 29 30 31 32, , , , , , , , , , , , , , , , , , , ,

Here the frame duration for the S-TDMA protocol is 21 slots instead of 32 slots

obtained in the previous case described in 4). Certainly, under the procedure outlined

above, some directed arcs receive more allocated slots than others (Tables TC2 and TC3

in Appendix C). The resulting schedule is termed the Basic Schedule (BS) since it serves

as a platform for traffic-sensitive S-TDMA in Section 4.3. In Figure 4.4, we observe that

the starting point in order to create this new approach is the Basic Schedule outlined

above. In Section 4.3, we will use the information provided by the load matrix to

enhance the Basic Schedule.


4.2 Network Delay of conventional spatial TDMA

The behavior of the S-TDMA is considered for non-traffic-sensitive slot assignment

policy in rough terrain. The average expected delay as a function of the total traffic for

S-TDMA for six terrain height parameters is shown in Figures 4.5 and 4.6. We can see

that a rougher terrain causes a higher propagation loss and has negative influence on the

network (decreasing the value of N ) connectivity as noted earlier. Normally, when we

increase σ , the TDMA schedule duration decreases as we will see later. The influence

of the routing algorithm and the traffic load should also be considered to study this

protocol.

In Figures 4.5 and 4.6, we examine how the average expected delay is affected by the

connectivity and traffic load. We observe that the ”lowest” network performance is

obtained when σ ≈ 60 m (e.g., network A). This could be due to the compromise

between the frame length Fd and the routing parameter h . Thus, starting from σ ≈ 0 as

the height parameter increases, the average expected delay is mainly determined by the

frame duration until a favorable number of hops ( h ≈ 1.85 hops) is reached. Around σ =

60 m, the routing and the schedule are then ”tuning” or working together in both

networks A and B, respectively.

In Figure 4.7, we show the network delay versus the connectivity for network C. We

observe in Figure 4.7.a that for N = 3.4 the delay is favorable for σ = 69 m. This

situation occurs with h =1.87 nodes as well. In summary, the results in our sample

networks show that there is a ”best” connectivity in the sense that the network delay is

highly improved for N ≈3.3 nodes combined with a corresponding h ≈1.9 hops. As

stated in [34], the routing algorithm plays an important role in the behavior of such a

network as well. If we reach a connectivity around 3.3 neighbors with their associated

parameter h ≈1.9 hops in our sample networks, we can achieved a ”good” combination

of the routing and the schedule in the sense that average expected delay exhibits better

performances as illustrated in Figures 4.5, 4.6 and 4.7. On the other hand, although we

may have less slots allocated for the schedule in the case σ = 100 m (e.g., the shortest

Fd in Figure 4.5). On average, a packet requires more hops ( h =2.22 hops) to reach the

final destination due to a lower connectivity ( N =2.8 nodes) which may increase the

network delay. For the numerical results we use the following basic set up described in

Table 4.1. A more detailed description is found in Appendix A.

Number of nodes 10

SIR threshold γ 0 10 dB

Number of arrival simulated events 10.000

Table 4.1 Basic simulation parameters.


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550

10

20

30

40

50

60

70

80

90

100

D in

times

lots

in packets\slotλ

áb c d

ef

Figure 4.5 (Network A). Average expected delay vs. the traffic load. Smoothnessparameter: ρ = 3 m. MAC protocol: Non-traffic-sensitive S-TDMA.

a) σ ≈0 m. Fd =66 slots. N = 7.6 nodes. h = 115. hops.

b) σ = 20 m. Fd = 37 slots. N = 4.8 nodes. h = 1.62 hops.

c) σ = 40 m. Fd =21 slots. N = 3.2 nodes. h = 1.88 hops.

d) σ = 60 m. Fd = 20 slots. N = 3.2 nodes. h = 1.88 hops.

e) σ = 80 m. Fd = 20 slots. N = 3.2 nodes. h = 1.88 hops.

f) σ = 100 m. Fd = 17 slots. N = 2.8 nodes. h = 2.22 hops.

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550

10

20

30

40

50

60

70

80

90

100

D in

times

lots

λ in packets\slot

a bc d

ef

Figure 4.6 (Network B). Average expected delay vs. the traffic load. Smoothnessparameter:ρ = 3 m. MAC protocol: Non-traffic-sensitive S-TDMA.

a) σ ≈0 m. Fd = 64 slots. N = 7.6 nodes. h = 1.15 hops.

b) σ = 20 m. Fd = 43 slots. N = 5.8 nodes. h = 1.35 hops.

c) σ = 40 m. Fd = 30 slots. N = 4.2 nodes. h = 1.64 hops.

d) σ = 60 m. Fd = 21 slots. N =3.4 nodes. h = 1.84 hops.

e) σ = 80 m. Fd = 19 slots. N =3.0 nodes. h = 1.93 hops.

f) σ = 100 m. Fd = 17 slots. N = 2.6 nodes. h = 2.15 hops.


2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 40

20

40

60

80

Connectivity

D in

tim

eslo

ts

a.

20 30 40 50 60 70 80 90 1000

20

40

60

80

terrain height parameter in m

D in

tim

eslo

ts

b.

Figure 4.7 (Network C) a. Average expected delay vs. connectivity for λ = 0 3. . b.Average expected delay as a function terrain height parameter. Smoothness parameter:ρ =3 m. MAC protocol: Non-traffic-sensitive S-TDMA.

As we have seen, one of the key performance parameters of the S-TDMA is Fd . To

further study this protocol, we would like to obtain the relationship between Fd and

the N for a set of networks. By using the models described in Section 2, we generated

random networks of N uniformly distributed nodes on the irregular terrain and plotted

Fd against the connectivity. The results from a simulation of 95 random networks are

shown in Figure 4.8. In this Figure, we approximate the results (depicted as stars) is by a

linear relation. If we increase the connectivity, the frame duration increases as well,

which is consistent with the fact that a network with higher connectivity produces more

arcs. This in turn means that more slots are required to cover all arcs at least once. From

our data, we derive the following approximation for the frame duration (solid line in

Figure 4.8):

Fd ≈ - 4 + 8.0 N⋅ (4.2)

where x denotes the largest integer less than or equal to x. For network A, N =3.2 and

Fd = 21.6 ≈ 21 slots, which fits the data well. This last Formula is valid for networks of

ten nodes. In this Formula we do not consider Fd for the case of flat terrain, i.e., σ ≈ 0.


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

20

25

30

35

mean # of neighbours

Fram

e du

ratio

n

Figure 4.8 The frame duration vs. connectivity. The number of networks is 95. Terrainparameters are: σ =100 m, ρ = 3 m. γ 0 10= dB. N = 10 nodes.

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

70

80

90

100

D in

tim

eslo

ts a

b

cd

e

λ in packets\slot

Figure 4.9 (Network A). Average expected delay in terms of λ for various values of

γ o (dB). Terrain parameters are: σ = 40 m, ρ = 3 m.

a) γ o = 5 dB. Fd = 29 slots. N = 4.2 nodes. h = 1.6 hops.

b) γ o = 7 dB. Fd = 29 slots. N = 4 nodes. h = 1.71 hops.

c) γ o = 10 dB. Fd = 21 slots. N = 3.2 nodes. h = 1.88 hops.

d) γ o = 12 dB. Fd = 21 slots. N = 3.2 nodes. h = 1.88 hops.

e) γ o = 15 dB. Fd = 21 slots. N = 3.2 nodes. h = 1.88 hops.


0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

70

80

90

100

D in

tim

esl

ots

a b

c

e

d

λ in packets\slot

Figure 4.10 (Network B). Average expected delay in terms of λ for various values of

γ o (dB). Terrain parameters are: σ = 40 m, ρ = 3 m.

a) γ o = 15 dB. Fd = 22 slots. N = 3 nodes. h = 1.933 hops.

b) γ o = 12 dB. Fd = 23 slots. N = 3.4 nodes. h = 1.84 hops.

c) γ o = 10 dB, (...). Fd = 30 slots. N = 4.2 nodes. h = 1.64 hops.

d) γ o = 7 dB. Fd = 37 slots. N = 4.2 nodes. h = 1.38 hops.

e) γ o = 5 dB. Fd = 38 slots. N = 5.6 nodes. h = 1.38 hops.

The average expected delay versus capture ratio, γ o (dB), is studied for networks A

(Figure 4.9), and B (Figure 4.10). In Figure 4.9, the lowest network delay situation is

achieved under the connectivity parameters discussed before for network A, i.e. N = 3.2

nodes & h = 1.88 hops, for the SIR threshold γ o = 10 dB. One can notice that γ o = 12, 15

dB have a similar connectivity parameters that the former case, but they do not

outperform the case γ o = 10 dB. This is due to the fact that in this case we have on

average more arcs per clique due to lower SIR target tolerates more interferes, which

might decrease the scheduling delay for some arcs. Therefore, if we have the situation

where several networks (using different values of γ o ) have the same connectivity

parameters we would select the network with the lowest SIR threshold γ o . In Figure

4.10, when is γ o = 12 dB, the network delay outperforms the other cases. Again, this

result agrees with the lowest network delay in Figure 4.6 since we have the same

connectivity parameters, too. So, we see that the main impact of the γ o is that it affects

the connectivity according to Eqn. 2.23.


4.3 Traffic-sensitive spatial TDMA

Utilizing traffic-sensitive S-TDMA schedules [15], where the slot assignment is

dependent on the amount of traffic P i( ) in each node i, is one way to further improve

network performance. Again, the network schedule can be viewed as a matrix where

the (i,j)th entry corresponds to the ith slot and the jth clique. The approach suggested in

this work is a combination of the basic S-TDMA protocol proposed in [12], together

with some extra slots allocated to the heavier loaded arcs to a great extend similar to the

study in [15]. Besides, the traffic-sensitive S-TDMA schedule will be termed Enhanced

Schedule (ES).

We use a fixed routing scheme (the MHA) to load the network. Under the uniform

traffic assumption, the total traffic that passes through each link of the network can be

estimated by counting the number of paths that use a certain link (i,j). We examine the

all the possible end-to-end connections or paths.

The algorithm we propose to create this kind of schedule has 8 steps:

Step 1: Compute the Basic Schedule (BS) of the net under study (Obtain Fd ). Count

the number of times an arc is enabled in the BS, this is its frequency in the BS.

Step 2: Calculate the load matrix (refer to Section 2.1.6). Sum the numbers, either in the

row or column that corresponds to each node i to obtain P i( ) .

Step 3: Select the maximum P i( ) , we name it, Pmax . Choose M max = # of neighbors of

the node with the Pmax .

Step 4: Reckon the Node Factor (NF) associated with node i, NF (i) = (4.3)

where x denotes the smallest integer greater or equal to x.

Step 5: Compute the duration of the traffic-sensitive frame as FES = (4.4)

Step 6: Subtract FES - Fd .These are the resultant or extra slots that will be added to the

BS, and they are assigned the cliques associated with heaviest loaded arcs

(see Fig. 4.4).

Step 7: Calculate the slots needed of each arc as follows:

Slots needed by link (i,j) = P ij( ) NF(i) / P i( ) (4.5)

P M

P

i( )max

max

NF ii

N

( ) =∑

1


Step 8: Assign the resultant slots from step 6 to the arcs with the lowest frequency in

the BS (step 1) and with the highest slots needed obtained in step 7. Add those

cliques which correspond to the selected arcs into the BS to have the ES.

We give an example to illustrate our algorithm, by considering network D (Appendix

D). First, we compute the BS associated with this network using the methodology

outline in Section 4.1.1. This BS has a Fd =17 slots (The description of the cliques are

given in Tables TC4 and TC5, Appendix C.3):

{ }S C C C C C C C C C C C C C C C C CD = 3 4 7 8 10 12 13 14 16 19 20 22 24 25 26 27 28, , , , , , , , , , , , , , , ,

Table 4.2 Load matrix for network D under uniform traffic.

node # P i( ) NF(i)

1 37 4

2 9 1

3 25 3

4 9 1

5 25 3

6 13 2

7 25 3

8 19 3

9 9 1

10 29 4

Table 4.3 Part of the figures to calculate the ES of net D. Note that the

sum of all NF(i):s is equal to 25 slots ( FES = 25 slots).

Node 1 2 3 4 5 6 7 8 9 10

1 0 0 0 0 6 0 16 6 0 9

2 0 0 0 0 9 0 0 0 0 0

3 0 0 0 9 0 4 0 0 0 12

4 0 0 9 0 0 0 0 0 0 0

5 6 9 0 0 0 0 0 4 0 6

6 0 0 4 0 0 0 0 8 0 1

7 16 0 0 0 0 0 0 0 9 0

8 6 0 0 0 4 8 0 0 0 1

9 0 0 0 0 0 0 9 0 0 0

10 9 0 12 0 6 1 0 1 0 0


Secondly, the load matrix of network D is given in Table 4.2. The P i( ) of each node is

then calculated from Table 4.2. For instance, for node 1 P i( ) sums to 37 (6+16+6+9).

The P i( ) for each node i is shown in Table 4.3. In the later table (step 3), node 1 has the

largest P i( ) = 37, this results in Pmax = 37 . Since node 1 has 4 neighbors, M max = 4

slots. Next, we employ Eqn. (4.3) to obtain the NF(i) of each node i in the network D

(step 4). If we add all NF(i):s in Table 4.3, we end up with 25 slots (steps 5, FES =25

slots), see (4.4).

According to step 6, FES - Fd = 25 slots -17 slots = 8 resultant slots. Further, we employ

(4.5) to calculate the slots needed by each arc of the network D. So generally speaking,

we map Tables 4.2 and 4.3 into Table 4.4 in terms of arcs since we are dealing with

link-activated schedules (step 7). In the column 2 of this Table we would like to

consider those arcs with an 1 ( frequency in the BS) and their respective slots needed

(column 4). To insure that we give an extra slot to a certain arc x, we would activate the

clique x in the S-TDMA frame, although it should be noted that one clique usually

activates more than one arc. We distribute the remaining 8 slots among the arcs as

follows (step 8). Select from Table 4.4, column four, those arcs with highest slots

needed which have the smallest frequency (e.g., 1). Note that for this network, the

chosen arcs are marked in bold in Table 4.4. In this way we select the following cliques

as the surplus cliques: C C C C C C C C4 8 10 13 19 24 25 26, , , , , , , . We denote the ES of network D

as SDES .

Thus, we end up with the following ES,

{ }S C C C C C C C C C C C C C C C C C C C C C C C C CDES = 3 4 4 7 8 8 10 10 12 13 13 14 16 19 19 20 22 24 24 25 25 26 26 27 28, , , , , , , , , , , , , , , , , , , , , , , ,

The average expected delay versus total traffic of SDES is depicted in Figure 4.11 (curve

b). We observe that for low traffic loads, SD (curve a) behaves better than SDES

probably due to the duration of the frame for the former case (25 slots) being longer that

the latter one (17 slots). However, the frame SDES has a more fair assignment with more

slots allocated to the arcs with expected heavier traffic. This might explain why SDES

performs better for higher traffic loads. One more possibility could be the frame SDDES ,

the ES of network D in other sequence or ”Distribution”, which works even better as we

can see in Figure 4.11 (curve c),

{ }S C C C C C C C C C C C C C C C C C C C C C C C C CDDES = 3 4 7 8 10 12 13 24 25 26 4 14 16 19 10 20 22 24 25 26 27 28 8 13 19, , , , , , , , , , , , , , , , , , , , , , , , ,

In the last ES ( SDDES ) we observe that the cliques are not in the same sequence as in SD

ES .

We obtain better network behavior if we distribute the remaining slots in such way to

reduce the number of slots the high loaded arcs will take to be enabled or to be repeated


again. However we will not elaborate on this issue. Moreover, the traffic-sensitive or ES

results might lead to higher network performance, in particular at higher traffic load

than the BS due to the adaptation of the slot assignment to the traffic load. Actually,

network D is a variation of network A in a higher terrain, we use this net due to it has

fewer arcs than network A.

arc # Frequency in BS P ij( ) Slots needed extra slots assigned

1 2 6 0.65

2 3 16 1.73

3 1 6 0.65

4 1 9 0.97 1

5 3 9 1

6 8 9 1.08

7 1 4 0.48

8 1 12 0.97 1

9 4 9 1

10 1 6 0.72 1

11 3 9 1.08

12 1 4 0.48

13 1 6 0.72 1

14 1 4 0.62

15 2 8 1.23

16 1 1 0.15

17 2 16 1.92

18 9 9 1.08

19 1 6 0.95 1

20 1 4 0.63

21 2 8 1.26

22 1 1 0.16

23 2 9 1

24 1 9 1 1

25 1 12 1.66 1

26 1 6 0.83 1

27 1 1 0.13

28 1 1 0.13

Table 4.4 (Network D) New approach of the traffic-sensitive S-TDMA.


0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

50

60

70

80

90

100

D in

tim

eslo

ts

λ in packets\slot

a b c

Figure 4.11 (Network D). Average expected delay vs. λ . Terrain parameters:σ =100

m,ρ = 3 m. γ o = 10 dB. MAC protocol: S-TDMA.

a) Basic Scheduling SD , b) Enhance Scheduling, SDES

, c)Enhanced Scheduling, SDDES

.

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

70

80

90

100

D in

tim

eslo

ts

a b

λ in packets\slot

Figure 4.12 (Network B). Average expected delay as a function of λ . Terrain parameters:

σ = 40 m,ρ = 3 m. γ o = 10 dB. MAC protocol: S-TDMA.

a) Basic Schedule, SB , and b) Enhanced schedule, SB

ES .


Figure 4.12 also plots the result of an assignment of this kind for network B (curve b)

where the ES by and large outperforms the BS of network B. In addition to that, in

Figure 4.13, we show the ES of network A (curve c) with similar results as in network

D. In summary, we can improve the network performance at higher traffic loads but

sometimes at the expense of increasing the average expected delay for low traffic loads.

4.4 Comparison of S-ALOHA and S-TDMA

In this Section, we compare S-ALOHA against S-TDMA for a given terrain and for the

same sample network. In Figure 4.13, we can see that S-ALOHA performs better for

low traffic loads than S-TDMA. On the other hand, for high traffic loads, S-TDMA

shows higher network performance. More specifically, for a traffic load of less than

approximately 0.40, the S-ALOHA shows less average expected delay than does the S-

TDMA policy. But for values between 0.4 and 0.6, it is apparent that S-TDMA is

superior, since the network delay is less. Why does the S-ALOHA perform better at low

traffic intensity ? The S-ALOHA algorithm does not require fixed allocated slots for

arcs as does S-TDMA. Therefore, at low values of λ , S-TDMA pays the price of greater

delay because the demand for slots tend to be overestimated.

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550

10

20

30

40

50

60

70

80

90

100

D in

tim

eslo

ts

λ in packets\slot

a b c

Figure 4.13 (Network A). Average expected delay vs. λ . Terrain parameters are: σ = 40m, ρ = 3 m. a) S-ALOHA with q*, b) S-TDMA Basic Schedule, c) S-TDMA Enhanced Schedule.


Even though some nodes handle only few packets, fixed slots are assigned to them

resulting in wasted slots within the frame. Since each node is allowed to transmit only in

its slots, the packet delay will be long in comparison with S-ALOHA. On the other

hand, at high traffic loads, the entire bandwidth will be effectively utilized by S-TDMA.

For λ > 0.4 , the collisions and retransmissions inherent in the S-ALOHA systems cause

it to incur greater delay more rapidly than the S-TDMA system. At higher traffic load

(0.4 < λ < 0.6), the structure of S-TDMA ensures that its delay increases in a more

orderly manner than S-ALOHA. In summary, the traffic load and the roughness

(different values of σ ) of the terrain have severe influence on the network performance

of the two MAC protocols under study. Comparison of the network performance shows

that network delay increases as the traffic load does, but S-ALOHA is more vulnerable

to the roughness of the terrain than S-TDMA. This is mainly due to the fact that in the

former case, there are larger number of transmissions occurring without the certainty of

being successful.

Chapter 5. Some Implementation Aspects

Chapter 5 Some Implementation Aspects Network connectivity depends on the link budgets, which means that other factors such as the transmitter power, and the antenna height can play significant roles in the network performance as well. In this Chapter, we discuss some of these practical aspects based on few studied cases. 5.1 Network performance versus transmitter power Transmitter power is an important resource in radio communication systems. First, we will study the transmitter power issue. In order to study this issue, we can rewrite Eqn. 2.23 in terms of the transmitter power in dBW.

( )Lo dB = ( )Pt dBW +135 > in order to have node i connected to node j (5.1)

( )Lij dB

Clearly we have the possibility to control the connectivity of a given network. For instance, by adjusting the transmitter power, it is possible to change the connectivity network figure N . For our sample networks, we now study the average expected delay in terms of the transmitted power thereby, changing the connectivity in the way outlined above. Two strategies will be used one that considers constant transmitter power for each node and one that keeps the received power at a constant level in each destination node. In the following analysis, we assume that the location of the nodes in the terrain and the communication requirements are known.

Pt

We now study the first transmitter power scheme. From Equation (2.21), we can see that the SIR is not affected by the transmitter power if we use the same power level and if we would neglect the noise power. Figure 5.1 (top) gives the network performance as a function of the transmitter power for the S-ALOHA protocol. We use the CONSTQ approach for the network under consideration (Network A). In Figures 5.1.b and 5.1.c, we observe the influence of the transmitter power on the S-TDMA protocol and the network connectivity, respectively. Also, in a given network of ten nodes at most 90 links are possible (fully connected network). In Figure 5.1 (bottom), our transmitter range (-5 dBW to 15 dBW) allow us to reach 80 % ( N ≈ 7 ) of the maximal possible connectivity. Clearly, it is very hard to

67


achieve a fully connected network since we are working with a quite rough terrain. Although we utilize very a higher transmitter power (i.e. 50 W), the network is still not fully connected. Thus, the results show that the average expected delay follows the connectivity as the transmitter power varies. Higher transmitted power may increase the connectivity, since we may be able to have more reliable links. However for S-ALOHA with a constant traffic load, higher connectivity might increase the network delay due to the increment of interference, since this causes, e.g., more collisions. One can say that the network goes from being range limited (low power) to interference limited (high power). Slow variations in the network behavior could be explain by the fact that S-ALOHA is driven by the CONSTQ policy described in Chapter 3, which is adaptive to the connectivity. Figure 5.1.b shows the impact of the transmitter power for the non-traffic-sensitive S-TDMA protocol in a studied case. In contrast to the S-ALOHA case, the former protocol is strongly influenced by changes in the connectivity. In Figure 5.1.b, we can observe the average expected delay as the connectivity increases. Around N ≈ 3 2. , the network delay is low. This means that we have a short frame duration combined with small number of hops to reach the intended destination. This part of the plot corresponds to a ”favorable” connectivity in agreement with the observations in Chapter 4. The right part of the network behavior in Figure 5.1.b illustrates that a longer frame is yielded by higher connectivity resulting in an increase in the average expected delay ( N > 4). In S-TDMA, sometimes may happen that changes of the connectivity yields fluctuations in network delay ( N ≈ 6). In contrast to this, S-ALOHA follows in a monotone way the increment of the transmitter power. For the S-ALOHA protocol, the network performance changes little as transmitter power varies. The second MAC protocol performs ”dramatically” different when the transmitter power changes. Connectivity is affected as well, and for some range the network delay improves due to certain "favorable" connectivity. We can formulate the two transmitter power approaches as simple ”power control” algorithms as well.

68


−5 0 5 10 150

5

10

15

Transmitter power in dBW

D in

tim

eslo

ts

a.

−5 0 5 10 150

10

20

30


D in

tim

eslo

ts

b.

−5 0 5 10 150

2

4

6


Co

nn

ectivity

c.

Figure 5.1 (Network A). a. Average expected delay in terms of the transmitter power. MAC protocol: S-ALOHA. b. Average expected delay in terms of the transmitter power. MAC

protocol: S-TDMA. c. Connectivity vs. Transmitter power. Total traffic load, = 0.25.

The SIR threshold is: = 15 dB. λ

γ o

Power Control Until now we have assumed that the transmitters of the nodes are all constant and the same. We denote this approach as PC1 PC1 (no power control) P ir ( ) = Transmitter power at node i = constant (5.2)

69


A second approach, PC2, maintains the received power ( ) a at constant level. We are therefore interested in how this algorithm works in our example nets. PC2 is described as follows

Pr

PC2 (constant received power) P jr ( ) = Received power at node j from the node i = constant (5.3)

Let us denote the constant receiving power as . In the MAC protocol, e.g. S-ALOHA, when a node decides to transmit in any slot, it must adjust its transmission power to hit the intended receiver j with . In the PC2 algorithm, the transmitter power of node i could be

Pro

Pro

P it ( ) = (5.4)

Pro ⋅(Gij )-1

where is the power gain between node i and j. Moreover, with PC2 we can see that average expected delay degrades in comparison with PC1 due to the higher probability of collisions (for S-ALOHA). In fact PC2 is in some sense, similar to the "no-capture" situation. In this case, collisions occur when two transmitting stations try to reach the same destination in the same slot. For network B, this alternative power is illustrated in Figure 5.2. In more detail, (curve a) the delay is around 10 slots for PC2 at whereas the delay remains around 7 slots for PC1 approach (curve b).

Gij

λ = 0 3.

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

45

50

D in

tim

esl

ots

λ in packets\slot

a b

70


Figure 5.2 (Network B). Average expected delay versus . MAC protocol: S-ALOHA. The

capture ratio, = 10 dB.

λγ o

a) PC2 approach ( W), and b) PC1 approach ( =-5 dBW). Pro =−10 10 Pt

Moreover, the PC1’s behavior is sensitive to the connectivity issue. Conversely, since PC2 keeps the same connectivity, only the traffic load affects its network performance. In Figure 5.2, we compare both approaches while we vary the traffic load. In this situation, PC1 achieves a lower delay than PC2. 5.2 Network performance versus Antenna height As mentioned earlier, we would like to briefly study the effect on the network performance by changing the antenna heights. By using a similar method as described before, we obtain the average expected delay versus antenna height for a certain range, namely, 1 m to 100 m. However, it should be noted that the flat earth propagation loss (Eqn. 2.5) in our propagation model is like a "periodic" function of the antenna heights [16,17], and we examine how network performance is affected by this factor. Starting with Equations (5.1) and (2.16), we have ( )L L Lmflat dri fs given link

2 2+ + < a reliable o dB t dBW (L ) = (P ) + 135 (5.5) With this approach, it is possible to vary the propagation loss (i.e., the ) by changing the antenna heights in the network, at the expenses of changing network connectivity as well. We use a constant antenna height for all nodes in the network. In Figure 5.3.a, we see a similar network behavior as in the Figure 5.1.a since the network delay follows the connectivity. Again S-ALOHA is operating according to the CONSTQ strategy. Note that we use different SIR threshold values in Figure 5.1 and 5.3. The main difference between Figures 5.1.a and 5.3.a is the fact that we have less connectivity control with the antenna height approach compared to the power adjustments. Also, it seems that the delay settles to constant value after an antenna height of about 20 meters. This is due to the fact the antennas then ”clear” minor obstacles in their surrounding. Figure 5.3.b shows results of the antenna height variation for the S-TDMA protocol (BS). We can observe that the relatively ”low” delay situation is reached for

L flat

N = 3.4 (antenna height = 12 m). However, in the S-TDMA we have the network delay ”oscillating” as N increases. As in Figure 5.1, the network performance here is greatly influenced by the connectivity which in turn is affected by the antenna height factor h in this case. t

71


0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

Antenna height in meters

D in

tim

eslo

ts

a.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30


D in

tim

eslo

ts

b.

0 10 20 30 40 50 60 70 80 90 1000

2

4

6


Co

nn

ectivity

c. Figure 5.3 (Network A). a. Average expected delay in terms of the antenna height. MAC protocol: S-ALOHA.. b. Average expected delay in terms of the antenna height. MAC

protocol: S-TDMA. c. Connectivity vs. antenna height. = 0.2. The capture ratio, =

10 dB. Terrain height parameter, = 40 m.

λ γ oσ

5.3 Practical Aspects So far, we have made several assumptions that would influence the implementation of the two MAC protocols concerned in real life radio networks. Here, we discuss three aspects: connectivity, data rate, and synchronization; and their limiting condition(s) regarding practical implementation. Let us start by consider the connectivity issue. In Chapters 3 and 4, we have seen that while changing the terrain height parameter, , for a certain fixed network we affect the network behavior in a great extent. In reality, we are mostly varying the diffraction losses in the network, this means changing the gain matrix in order to study its impact on network performance. So, if we are increasing , we end up with a more mountainous terrain which increases the component (Eqn. 2.16) in the total path

σ

σ

driL

72


73

loss. However, in a real network, this is not possible since the terrain is hardly changeable. The former procedure (varying σ ) is in fact an artificial way to change the connectivity. Ideally, if we would like to match the suitable connectivity derived from a given value of σ to the connectivity yielded by the transmitter power (PC1) or antenna height approach. In other words, we want to determine which connectivity is useful to obtain a certain network performance. We can utilize the method described in this Chapter to obtain the particular value of the N , or the h or a useful combination of both. For S-TDMA, these mechanisms of controlling the network connectivity are beneficial to the network designer. From a practical point, it is possible to measure the gain matrix in a stationary packet radio network. Of course there are more ”natural” ways of changing the connectivity on individual basis, e.g., by means of moving some nodes to improve the network performance. These cases have not been considered in our study for sake of simplicity. In our calculations we has assumed a data rate of 100 Kbits/s (current packet radio networks such as GRAPES [41] can handle about 120 Kbits/s with more efficient modulation schemes). So, although the proposed data rate is not currently available, it seems reasonable to be assumed for wireless data communication services. Since with this data rate we take care that the delay spread [42] in this kind of channel is less than the symbol transmission time, which imply that the Inter Symbol Interference (ISI) may be neglected. Since slotted systems have been addressed, we should also note that synchronization in a packet radio network implies that each slot has associated with it a guard interval that is used to compensate the varying geographical distance between the nodes. The lost of capacity for this guard band is not considered in our simulations. Also, regarding the antenna height we must be aware that Ladell’s model [19] is valid only for antenna heights of up to 50 m. This means that if we want to further study the impact of the antenna heights, we should use another model for the modified flat earth propagation loss, for instance [39].

Chapter 6 Conclusions and discussion

In this thesis two different kinds of channel access protocol in multihop packet radio network in rough terrain are investigated: S-ALOHA and S-TDMA. In some sense these two protocols are extremes among all the MAC protocols. We use a fixed routing strategy, the Minimum Hop Algorithm and given network topologies. A non-binary connectivity, that includes a detailed radio propagation model which takes the interference screening of the terrain obstacles into account, together with a simple model of queues in each node were the basis of the evaluation of the two MAC protocols. Thus, we mainly study through computer simulations the effect of various factors (terrain profile, propagation model, the transmitter power, transmission probabilities/schedules and traffic load) on the network performance measure, the average expected delay. We also consider optimising the network performance, of the MAC protocol with respect to the transmission probability. We noticed that increasing the roughness of the terrain had a negative influence on the connectivity of a network. In general, under the condition that the network is still connected, we saw that the behaviour of the two access protocols is different. When the roughness parameter is increased the network delay increases for low traffic loads for S-ALOHA. Conversely for higher traffic loads, the network delay behaves better for a rougher terrain with a connectivity around 3.2-3.4 neighbours. For S-TDMA the network delay usually varies from high delay to low delay to high delay again as the connectivity decreases. This behaviour arises from the trade-off between the routing and the schedule which affects the average expected delay as it is explained in Section 4.2. Moreover, the rougher the terrain, the more the expected number of hops increases. This extends the number of slots to reach the final destination, which reduce the probability of successful transmissions in the next hop yielding higher network delay for S-ALOHA. Even so, we might face a similar situation regarding the number of hops in S-TDMA, the frame duration mostly decreases when increases. However, in our sample networks there is a certain connectivity that is most favourable with respect the network delay in S-TDMA. This case not correspond to the ”minimal” length of the transmission schedule, but to a ”good” combination of the frame duration and the routing algorithm.

σ

Conclusions and discussion

As was expected, the results show a trade-off for the network performance. On one hand, S-ALOHA is very good for low traffic loads, on the other hand, for high loads, S-TDMA shows higher performance. Principally, the difference is due to the fact that S-ALOHA for low traffic conditions the contention mechanism of S-ALOHA works well (for a "reasonable" q). This protocol will manage to maintain successful transmissions while the waiting time in queue will be short in comparison with the waiting time of the S-TDMA, which is upper bounded by the duration of the frame. But, in the case of high traffic loads, the waiting time in the queues is the other way around, and the delay of S-ALOHA will rise steeply with the load. For the S-ALOHA protocols we have studied two strategies to choose their controlling parameter, the transmission probability, q. One approach considers the use of the same q for all the nodes in the network. The second approach assigns a transmission probability , for each node i, accordingly to a partition scheme derived from the load matrix introduced in Chapter 2. The former assignment, abbreviated CONSTQ, yields a ”nearly” optimal performance for the network delay. In our samples networks, the VARQ2 approach slightly outperforms CONSTQ, even though it has not been optimised in our study. Moreover, VARQ2 was better with respect to the throughput at high loads than the former approach. Further improving node adaptive or even link transmission policies might further studies.

q i

For S-TDMA, we have proposed two new procedures to find the transmission schedules namely the classical or non-traffic-sensitive S-TDMA and the traffic-sensitive S-TDMA. We saw, that later approach performances better than the classical one, and it produces more ”fair” transmission schedules. We also saw the need to couple the routing algorithm to the MAC protocol. Further studies might consider the order of the cliques within the S-TDMA frame aiming to reduce the scheduling time, this is the time window between one link-activation and the next turn to transmit its traffic. Finally, the connectivity issue has been discussed briefly. Mainly, the transmitter power and the antenna height are used to control the connectivity. We noticed that the S-TDMA is more sensitive to the transmitter power variations than the S-ALOHA where we employ the CONSTQ policy. In the power study, we saw that the use of the same transmitter for the node of the network is better than the policy of having constant received power assignment. The antenna height approach permits less connectivity variation within range under study in comparison with the transmitter power. It is very interesting, in particular for S-TDMA, the possibility to control the connectivity, since we will able to adjust or to tune it to obtain the favourable N to improve the packet

76

Conclusions and discussion

77

delay. However, a more realistic approach might consider changing the transmitted power and/or the antenna height individually. Interesting future work could be to find how much power should each node use (local power control) to reach a certain required network performance in both two MAC protocols. A solution in the bursty traffic situation in mobile systems for the power control [38] can be applied to the S-ALOHA case. Also, the use of directional antennas is an attractive topic for further studies to enhance the capacity of multihop PRN:s. These antennas may reduce the interference at the other neighbours of a particular node, when it tries to reach one of them. Furthermore, traffic-adaptive routings in these MAC protocols will improve the multihop radio network performance. The impact of error correction techniques and the modulation schemes could be also addressed. Distributed or adaptive S-TDMA schemes can be considered as well, which takes advantage of their local surroundings.

References [1] Khan, E., "The organization of computer resources into a packet radio

network", IEEE Trans. Commun., vol. COM-25, Jan 1977. [2] Fifer, W.C., Bruno, F.J.,”The low-cost packet radio”, Proc. IEEE, Jan.

1987, pp. 33-42. [3] Takagi, H., Kleinrock, L., "Optimal transmission range control for

randomly distributed packet radio terminal". IEEE Trans. on Comm., COM-32, March 1984.

[4] Tobagi F.A., "Multiaccess protocols in packet communication systems",

IEEE Trans. Comm.,COM-28 April 1980. [5] Hou, T-C, Li, V.O.K., "Transmission range control in multihop packet

radio networks", IEEE Trans. Comm., COM-34, Jan 1986. [6] Kleinrock, L., Silvester, J.,"Optimum transmission radii for packet radio

networks or why six is a magic number", Proc IEEE Nat Telecomm Conf, Dec 78, pp. 4.3.1-4.3.5.

[7] Abramson, N.,” The ALOHA system- Another alternative for computer communications”, 1970 Fall Comput. Conf. AFIPS Conf. Proc., vol. 37 Montval, NJ : AFIPS Press, 1970, pp. 281-285. [8] Roberts, L.G.," ALOHA packet system with or without slots and

capture", Comput. Commun. Rev., vol. 5,1975. [9] Klienrock, L.,Silvester, J. A.,"On the capacity of multihop slotted

ALOHA networks with regular structures", IEEE Trans Comm., vol. COM-31, No. 8, pp. 974-982, August 1983.

[10] Nelson, R., Kleinrock, L.,"The spatial capacity of a slotted ALOHA

multihop packet radio network with capture", IEEE Trans Comm.,COM-32, June 84.

[11] Shiao, F.-M., Yee, J.R.," An algorithm to find optimal routing

assignment for class of PRNs" ICC's 1991, pp.1604-8 vol. 3. [12] Nelson, R.,Kleinrock, L.,"Spatial-TDMA: A collision free multihop

channel access protocol", IEEE Trans Comm.,COM-33, Sept 1985. [13] Cidon, I., Sidi, M.," Distributed assignment algorithms for multihop

packet radio networks", IEEE Trans Computers, Vol. 39 , October 1989.

References

[14] Ephremides, A.,Truong, T., "Scheduling broadcast in multihop radio

networks", IEEE Trans. on Comm., vol. 38, No. 38 April 1990. [15] Robertazzi, T., Shor, J. "Traffic sensitive algorithms and performance

measures for the generation of self-organizing radio networks schedules" IEEE Trans on Comm., vol. 41, No. 1 Jan. 1993.

[16] Zander, J.,"Jamming in multihop packet radio networks", IEEE Trans.

on Comm., COM-39, October 1991. [17] Kuperus, F., Arnbak, J.,"Packet radio in a Rayleigh channel", Electron.

Letter., vol. 18, pp. 506-507, June 1982. [18] Roobol, C., "Multihop packet radio networks in random terrain:

connectivity and some terrain adaptive routing algorithms", Milcom'93 , pp. 428-431, Conference record vol.2.

[19] Ladell.L.,”Transmission Loss predictions in wooden terrain ”, Proc.

NRS 86, Stockholm, Sweden. [20] Tobagi, F.,” Modelling and performance analysis of multihop packet

radio networks ”, Proc. of IEEE, Vol. 75, No. 1, 1987. [21] Shacham, N., "Stochastic models for multihop packet radio networks",

Stochastic analysis of computer and communications systems, pp. 733-65. H. Takagi , Editor, Elsevier Science Publishers B.V. (North Holland).

[22] Jubin, J., Tornow, J.D.,"The DARPA Packet Radio Network Protocols",

Proc. of the IEEE, vol. 75, No. 1, Jan. 1987. [23] Beyer, D.A.,” Accomplishments of the DARPA SURAN program”, Milcom'90 , pp. 855-862, Conference record vol.2. [24] American Radio Relay. AX.25 Amateur Packet-Radio Link-Layer

Protocol, version 2.0, Newington, CT,1984. [25] Karn, P., Price, H., and Diersing, R.,"Packet Radio in the Amateur

Service", IEEE Journal on Selected Areas in Communications, May 1985.

[26] Bertsekas, D.,Gallager, R.,"Data Networks", Prentice Hall International;

2nd Edition. 1987. [27] Woerner, B. D., Jeffrey, H.R., Rappaport, T.S.,"Simulation issues for

future wireless modems", IEEE Comm Magazine, vol 32, No. 7 July 1994.

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[28] Zander, J.,"Performance of optimum control in cellular radio systems", IEEE Trans. Veh Tech.,VT-41, February 92.

[29] Jeruchim, M.,Balaban, P.,Shanmugan, S.,"Simulation of

Communication Systems", Plenum 1992. [30] Kleinrock, L., Silvester, J.,"Spatial reuse in multihop packet radio

networks", Proc. of the IEEE, Vol. 75, No. 1, Jan. 1987. [31] Parson,D.,”The mobile Radio Propagation Channel ”. London. Pentech Press, 1992. [32] Lee,W.C.Y.,”Mobile Cellular Telecommunications Systems ”. New

York. McGraw Hill, 1989. [33] Zander , J., Ahlin L.,”Radio Communication Systems”. Royal Institute of Technology”. February 1995. Stockholm. [34] Wieseltier, J., Barnhart, C., Ephremides, A.,”A neural network approach

to routing without interference in multihop radio networks”. IEEE Transactions on Communications, vol. 42,No.1 Jan. 1994.

[35] Silvester, J., Wang, J.,”Throughput optimization in single commodity

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[36] Somarriba, O.,” Packet delay in multihop radio networks in rough

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[38] Zander, J., Rosberg, S.,”Power control in wireless networks with

random Interferes”, Internal report, Dept. of Signals, Sensors and Systems, Royal Institute of Technology, Sweden, September 1995.

[39] Longley, A.G., Rice,P.L., “Prediction of tropospheric radio transmission

loss over irregular terrain”, ESSA Tech. Rep. ERL 70 ITS 67 ITS Boulder Colorado, 1986.

[40] Sklar, B., “Digital Communications” , Prentice Hall Internationa

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York, 1990.

Appendix A

Appendix A Performance evaluation A.1 Introduction The simulation is performed as follows: We first generate a new terrain where the random location of the nodes is taken from a uniform distribution. Then, we apply the propagation model mentioned in Section 2.1.3 to obtain the gain link matrix of the network. In this point it is very important to verify if our network is connected (we use the threshold path loss), which means that a packet will reach its final destination in a finite number of timeslots. From this, we are able to draw the connectivity diagram of the PRN:s, e.g., Figure 2.6. Next, it is time to turn our attention to the routing strategy that performs routing based on the gain matrix; The information is summarized in the routing matrix. Each node knows to which neighbor it must transmit in order for a given packet to reach its final destination. On the other hand, the queueing aspect will be examined as well. Thus, we start the simulation with empty buffers, we assume that each node has its own buffer where packets can stored until the node is able to transmit the packet successfully. For each slot the channel access protocol (S-ALOHA or S-TDMA) generates a set of nodes transmissions according to the explained in Chapters 3 and 4. In the S-ALOHA approach, the results of these transmissions are evaluated using Equation 2.21; For the case of S-TDMA we already know that every transmission is coordinated to succeed. If a transmission is successful two events can happen: First, a packet has to "go" to an intermediate node, which means that we only need to "move" the concerned packet to the queue of the node in transit. In the second variant, if the packet arrives at its final destination, then the packet leaves the network immediately. Our concern is how many slots on average it takes a packet to successfully reach its final destination counting from the particular slot that was generated it, in the originated node. In the S-ALOHA scenario, we will use a simulation time of 10000 slots after a 1500 slots of warm-up time, for each combination of and D (one single run simulation). The same procedure is used for S-TDMA except for the warm-up period of 1000 slots. To reduce the variance in the results we make a batch of 100 simulations of the 10000 slots i.e. each point on the curves in ,e.g. Figure 3.3, is based on 1.000.000

λ

83

Appendix A

slots. Furthermore, if we obtain n random samples of average expected packet delay in the simulations, they are , ,...., The sample mean [29] is equal to (we use

n=100),

D1 D2 Dn

]n( )

Var DiI

n

∑= =1 n

n=2

[D ]

[ ]( )1

(n)

D nD

ni

i

n

( ) =∑=1 (A.1)

We can also obtain the sample variance as,

[ ]S n

D D n

ni

i

n

2 1

2

1( )

( )=

−∑

−=

(A.2) The variance of D , [Var D could be estimated from the following formula (assuming

that the samples of the average expected delay are identical independent distributed),

[ ]Var D n Varn

Dn ni

n

iD

D( ) ( ) ( )= ∑ = =1 1 1

12

22

σσ

(A.3)

Furthermore, an unbiased of Var is obtained by replacing in equation (A.3) by

(n), resulting in

n( ) σ D2

S 2

[ ]$ ( ) ( )Var D n S nn

D D

n ni

i

n

= =−∑

−=

22

1

(A.4)

84

Appendix A

85

A.2 Simulation Parameters The simulations have been performed using a discrete event simulator written in PASCAL programming language. The simulation parameter are displayed in Table A.1. The warm-up time is the number of initial arrival that occur before the logging of the results starts. Result logging is stopped when the last arrival occurs. All the results are average over the number of independent runs. The typical relative error for results in Chapter 3 was 1%, in Chapter 4 it was 1 %, and in Chapter 5 was 1.5 %.

Simulation Parameter Value Number of nodes, N 10 Transmitter Power - 5 dBW Antenna height 20 m Relative permittivity 5 Frequency 300 MHz Typical threshold path loss 130 dB Noise level at the receiver 1.2x10 -14

W Results Chapter 3 SIR threshold γ O 10 dB Number of simulated arrival events 10000 Warm-up period (arrival events) 1500 Number of independent runs 100 Results Chapter 4 SIR threshold γ o 10 dB Number of simulated arrival events 10000 Warm-up period (slots) 1000 Number of independent runs 100

Table A.1 Simulation parameters.

Appendix B S-ALOHA support

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

D in tim

eslo

ts

λ in packets\slot

a b cd

Figure B.1 (Network B). Average expected delay vs. , with q as a parameter. The

capture ratio is: = 10 dB. The noise power is used in the simulations when

interference is present.

λγ o

a) q = 0.5, b) q = 0.4, c) q = 0.3, d) q = 0.2.

Appendix B

88

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

q

Ave

rag

e q

ue

ue

len

gth

a

b

c d

Figure B.2 (Network A. Average queue length vs. q, with as a parameter. The

capture ratio is: = 10 dB. λ

γ oa) = 0.4, b) = 0.3, c) λ = 0.2, d) = 0.1. λ λ λ

Appendix C S-TDMA support C.1 Calculations of S-TDMA Schedule for the example network A. We now examine Figure 2.4 as our network example A. Further, in Figure 2.4 the connectivity diagram is depicted. The threshold loss value is assumed to be 130 dB. From this diagram we can generate the directed connectivity graph as we can see in Figure C1. In this figure, in parenthesis is what we have termed directed arc, e.g. the directed arc 1 is the unidirectional link from the node 1 to the node 5; Conversely the unidirectional link from node 5 to node 1 is the directed arc 10. Moreover, Figure C2 shows the compatibility matrix. From this matrix is possible to derive the set of all the maximal cliques as it is summarized in Table CT1.

8

10

6

1

7

9

4

3

2 5 (3)

(2)

(18)

(25)

(20)(26)

(27)(4)

(32)

(8)

(28)

(9)

(6)

(21)

(24)

(31)

(22)

(12)

(5)

(11)

(29) (13)

(17)

(10)

(1)

(19) (15)

(14)

(7)

(30)

Legend:

# , Node # ...

, Directed arc.

( # ), Arc. # Figure C1 Directed connectivity graph of network A (Figure 2.4).

81

CM =

10000100000000010001000000000000

01001100000000000000000000000000

00101100000000000001000000000000

00011000000000000000000000000000

01001100000000000001000000000000

10000100000000010001000000000000

00001010000000000000000010000000

00001001000000000000000000000000

10000000100000010001000000000000 00000100010000000000000010000000

01000100001000000000001000000000

00000100000100000001000000000000

00000000100010000010000000000000

10000000000001000001000000000000

00001100000000100000000000000000

10000100000000010001000000000000

00001000100000001001000000000000

00001100000000000100000000000000

00001000100000000010000000000000

10000100000000010001000000000000

00000100000000100000100000000000

00000100000000100000010000000000

01000100001000000000001000000000

00000000100000000001000100000000

00101100000000000000000010000000

00000000100000000000000001000000

00000100000000000000000010100000

01000000001000000000001000010000

00000100000000100000000000001000

01000000101000000000000000000100

00000100000000000001000000000010

01000000100000000000000000000001

Figure C2 The Compatibility Matrix (CM) of the sample network A. From the Compatibility Matrix in C2 we can get in a straightforward manner the set of all maximal cliques from each row. These are listed below in Table CT1, C1 = 1, 6,16,20{ } C2 = 2,5,6{ }

C3 = 3,5,6, 20{ } C4 = 4, 5{ } { }C5 2 5 6= , , C6 = 1,6,16,20{ }

C7 = 5,7,25{ } C8 = 5, 8{ }

C9 = 1,9,16,20{ } C10 = 6,10,25{ }

C11 = 2,6,11, 23{ } C12 = 6,12,20{ }

C13 = 9, 13,19{ } C14 = 1,14,20{ }

C15 = 5,6,15{ } C16 = 1, 6, 16, 20{ }

C17 = 5, 9,17,20{ } C18 = 5, 6,18{ }

C19 = 5, 9,19{ } C20 = 1,6,16, 20{ }

C21 = 6,15, 21{ } C22 = 6,15,22{ }

C23 = 2,6,11,23{ } C24 = 9,20,24{ }

C25 = 3,5,6,25{ } C26 = 9,26{ }

C27 = 6,25,27{ } C28 = 2,11,23,28{ }

C29 = 6,15,29{ } C30 = 2, 9,11,30{ }

C31 = 6,20, 31{ } C32 = 2, 9,32{ }

Table TC1 The set of all maximal cliques for the example network A.

82

Arc # Repetition Arc # Repetition 1 6 17* 1 2 6 18* 1 3 2 19 2 4 * 1 20 11 5 12 21* 1 6 15 22* 1 7* 1 23 3 8* 1 24* 1 9 7 25 3 10* 1 26* 1 11 7 27* 1 12* 1 28* 1 13* 1 29* 1 14* 1 30* 1 15 3 31* 1 16 3 32* 1

Table TC2. The set of all arcs and their repetition (frequency in the BS) in the CM for the example network A. The asterisk marks the arc numbers which correspond to the untouchable cliques (e.g., arc 4* means clique 4 is an untouchable).

In other words, the Skeleton schedule of net A is :

{ }Skeleton schedule C C C C C C C C C C C C C C C C C C = 4 7 8 10 12 13 14 17 18 21 24 26 27 28 29 30 31 32, , , , , , , , , , , , , , , , ,

Arc # Repetition Arc # Repetition 1 1 17 1 2 3 18 1 3 0 19 1 4 1 20 4 5 3 21 1 6 8 22 1 7 1 23 1 8 1 24 1 9 6 25 3 10 1 26 1 11 2 27 1 12 1 28 1 13 1 29 1 14 1 30 1 15 3 31 1 16 0 32 1

Table TC3 The coverage of the skeleton schedule for the example network A. In bold the arcs (i.e., arc 3 and arc 16) no covered yet by the skeleton schedule.

83

Using the information in Tables TC1 and TC3, we therefore add arcs 3 and 16 to the skeleton schedule to come up with the Basic Schedule (BS) of network A:

{ }S C C C C C C C C C C C C C C C C C C C C CA = 3 4 7 8 10 12 13 14 16 17 18 21 22 24 26 27 28 29 30 31 32, , , , , , , , , , , , , , , , , , , , C.2 Tables for network D in section 4.3.

arc # head node tail node arc # head node tail node 1 1 5 15 6 8 2 1 7 16 6 10 3 1 8 17 7 1 4 1 10 18 7 9 5 2 5 19 8 1 6 3 4 20 8 5 7 3 6 21 8 6 8 3 10 22 8 10 9 4 3 23 9 7 10 5 1 24 10 1 11 5 2 25 10 3 12 5 8 26 10 5 13 5 10 27 10 6 14 6 3 28 10 8

Table TC4 Description of the unidirectional arcs for network D in section 4.3 .

{ }C1 1 6 1518= , , , { }C2 2 5 6= , , { }C3 3 5 6 18= , , , { }C4 4 5 18= , ,9, { }C5 2 5 6= , , { }C6 1 6 1518= , , , { }C7 1 7= , { }C8 5 8 17= , , { }C9 1 1518= ,9, , { }C10 6 10 15= , , { }C11 2 6 11= , , ,21 { }C12 6 12 18= , , { }C13 9 1318= , , { }C14 114 18= , , { }C15 1 6 15= , , { }C16 5 16 18= ,9, , { }C17 5 6 1517= , , , { }C18 1 6 1518= , , , { }C19 6 19= , ,23 { }C20 6 18= , ,20 { }C21 2 6 11= , , ,21 { }C22 9 18= , ,22 { }C23 1= ,23 { }C24 6= ,23,24 { }C25 2 11= , ,21,25 { }C26 6 1518= , , ,26 { }C27 2 11= ,9, ,27 { }C28 6 18= , ,28

Table TC5 The set of all maximal cliques for the example network D in section 4.3.

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Appendix D Sample nets

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dist

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Figure D.1 Contour plot of the terrain and Network C. Terrain parameters are: =40 m, σρ = 3 m. The circles indicate the position of the stations, which are numbered

1,2..10. The lines represent the connections among the nodes.

5 10 15 20 25

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Figure D.2 Contour plot of the terrain and Network D. Terrain parameters are: =40 m, σρ =3 m. The circles indicate the position of the stations, which are numbered 1,2..10.

The lines represent the connections among the nodes.

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