1

Static and Dynamic Resource Allocation

in a Multiservice Satellite Network with Fading®

Nedo Celandroni°, Franco Davoli*, Erina Ferro°

°ISTI-CNR, Area della Ricerca del C.N.R., Via Moruzzi 1, I-56124 Pisa, Italynedo.celandroni@cnuce.cnr.it

erina.ferro@cnuce.cnr.it*Department of Communications, Computer and Systems Science (DIST)

University of Genoa, Via Opera Pia 13, 16145 Genova, Italyfranco@dist.unige.it

Abstract: A control architecture for resource allocation in satellite networks is proposed, along withthe specification of performance indexes and control strategies. The latter, besides being based oninformation on traffic statistics and network status, rely upon some knowledge of the fading conditionsover the satellite network channels. The resource allocation problem consists of the assignment, by amaster station, of a total available bandwidth among traffic earth stations in the presence of differenttraffic types. Traffic stations are assumed to measure continuously their signal fade level, but thisinformation may either be used only locally or also communicated to the master station. According tothe information made available on-line to the master station on the level of the fading attenuation ofthe traffic stations, the assignment can be made static, based on the a priori knowledge of long-termfading statistics, or dynamic, based on the updated measurements. In any case, the decisions can beadapted to slowly time-varying traffic characteristics. At each earth station, two basic traffic types areassumed to be present, namely guaranteed bandwidth, real-time, synchronous data (stream traffic), andbest effort traffic (datagram traffic). Numerical results are provided for a specific architecture in thedynamic case, in a real environment, based on the Italsat satellite national coverage payloadcharacteristics.

Keywords: Satellite Communications; Fade Countermeasures; Bandwidth Allocation; Call AdmissionControl.

1. Introduction

In multiservice broadband networks, in order to support different classes of traffic, characterized bydiverse statistical nature and Quality of Service (QoS) requirements, in the presence of limitedresources (buffers, bandwidth, or processing capacity), several forms of control are exerted tomaintain a desired level of performance for all users and traffic types. Moreover, to cope with possiblevariations in bandwidth demand and offered load, control actions should be devised to be dynamic,based on instantaneous and past information, or, at least, adaptive in nature. This control scenariomeets with still another one in networks involving satellite channels. Here, dynamically varying fadingconditions, caused by adverse atmospheric events (e.g., rain, hail or snow) can heavily affect thetransmission quality, especially when working in Ka band [20 – 30 GHz], unless adaptive fadecountermeasure techniques are adopted. In essence, fade countermeasures address the physical layerrequirement of keeping the Bit Error Rate (BER) below a given threshold, whatever the channeldegradation may be, within a certain operating range, beyond which the station is declared to be inoutage conditions.

Several methods have been studied in the literature and effectively applied to provide compensationfor rain attenuation [1, 2]; among others, we recall using additional transmission power (up-power

® Work supported by the Italian National Research Council (C.N.R.), under the “5%” Multimedia Program.

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control), and using a portion of the system bandwidth to have a rain margin. The latter may be used toincrease the data coding rate for stations that temporarily suffer heavier attenuation, by adoptingappropriate Forward Error Correction (FEC) codes in order to maintain the desired BER level, even bydecreasing the information transmission rate, if necessary, when no more spare bandwidth is available.

On the other hand, controls applied to cope with variations in traffic dynamics and with the presenceof multiple services, in order to guarantee potentially different performance requirements and to avoidcongestion, typically act at protocol layers from 2 above, spanning data link, MAC, network,transport, and even the application layers. In many cases, the choice of where, how and for whatpurpose to exert a control action depends on the type of traffic to be dealt with and on the extent ofservice separation, as opposed to complete statistical multiplexing, that is adopted for packetizedtraffic [3, 4]. In particular, in the presence of both guaranteed bandwidth and best-effort flows (eitherderiving from elastic traffic, like TCP connections, or from non-guaranteed real-time applicationsusing UDP), the probability of blocking connection requests and the loss of data units in buffers aretwo performance indexes that deal with the different nature of the traffic involved and span widelydifferent time scales. A typical control that is exerted in the real-time traffic case is on the admissionof new guaranteed bandwidth requests (Call Admission Control, CAC), by taking into account bothperformance indexes (see, e.g., [5 – 10]). Whenever service or user separation is applied to someextent, the issue of bandwidth allocation should also be taken into account.

In this paper, we consider some possible approaches that essentially combine the physical layeractions related to fade countermeasures with CAC and bandwidth allocation. The emphasis is on adecentralized administration of the assigned bandwidth, with some kind of hierarchical coordination.Satellite networks almost naturally lend themselves to this kind of approach, as the earth stations arescattered on a wide area and, at the same time, a master station, playing the role of a coordinator, isusually present. In general, we have a resource allocation problem, consisting of the assignment of atotal available bandwidth among the earth stations and, inside them, among the traffic types. Wedistinguish two situations, as regards the information available on-line to the master station on thelevel of fading attenuation of the traffic stations. According to this, the assignment can be made static,i.e. based on the a priori knowledge of long-term fading statistics, or dynamic, based on fresh valuesof the attenuation levels of the traffic stations. In either case, it is possible to adapt the assignment on-line to slowly time-varying traffic characteristics. At each earth station, two basic traffic types aresupposed to be present: i) guaranteed bandwidth, real-time, synchronous traffic (stream traffic),generated by voice and video applications, and ii) non-guaranteed bandwidth, non real-time,asynchronous traffic (datagram traffic), produced by data applications. Some previous work in thissetting has been done in [2, 11], where, however, a centralized control case is considered, and [12],which addresses the static assignment with reduced information on instantaneous fading.

The paper is organized as follows. The models of our satellite network and of the faded channel arepresented in the next Section. The models of the considered traffic types along with the relevantperformance measures are presented in Section 3. Section 4 illustrates the time scales we have to dealwith in treating the problem. Section 5 describes the control architecture, while Section 6 considers thehierarchical dynamic bandwidth assignment, whose numerical results are presented in Section 7, withdata taken from a real case. Section 8 concludes the paper and gives the directions for future work.

2. Satellite Network Models: Static and Dynamic

We consider a fully meshed satellite network that uses bent-pipe geostationary satellite channels,joining N traffic stations. This means that the satellite only performs the function of a repeater,without on board processing of data. The system operates in MF-TDMA (Multi Frequency-TimeDivision Multiple Access) mode, which allows us to divide the system capacity C into a number ofchannels, so that the traffic stations can be downsized with respect to a pure TDMA system. A trafficstation cannot, however, transmit simultaneously on different TDMA carriers in the same temporalslot, because it is assumed to have only one modulator. The total transmission capacity of each stationis thus limited to that of one carrier. A master station maintains the system synchronization and isresponsible for the capacity allocation to the traffic stations. The master station performance is the

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same as the slave stations’ one, so that the role of master can be assumed by any station in the system.This assures that the master operates in clear sky conditions for almost all of the time, because whenthe current master’s attenuation exceeds a given threshold, its role is assumed by another station that isin good conditions. The fade countermeasure system adopted is based on the up-link power controland on the data coding and bit rate changes. The multimedia data transmissions between the trafficstations occur in temporal slots assigned by the master, each one generally on different TDMA carriers(frequencies).

2.1 Fade modeling

The effect of fading (on the up-link beyond up-link power control range, and on the down-link of eachchannel) is modeled as a reduction in the bandwidth actually “seen” by a traffic station, or,equivalently, by an increase in the bandwidth required by the traffic sources to maintain the sameQuality of Service. As such, in general, this effect may cause a station to “see” synchronous traffic atmultiple rates, even though all synchronous data sources at an earth station had the same peakbandwidth. We will return to this point later on, when touching upon the possible bandwidth allocationstrategies. For the sake of notational simplicity, we assume for the time being that each station onlysees a single type of attenuation, as if the fading were of up-link-predominant type. In order to avoid toomany oscillations in applying the fade countermeasures according to each single fade level variation, weassume that the measured level of the signal attenuation be categorized in a class “level”,characterized by the fact that the countermeasure strategy adopted remains unchanged for all the levelsof signal attenuations belonging to that class. Thus, a fade class aggregates fade levels that require thesame data redundancy. The effect of the latter, at station i, may be expressed by a coefficient rlevel

(i ) , or

by its inverse

†

blevel(i ) , which expresses the reduction in bandwidth “seen” by the station. For each station

i, the "level" value may range from 1 up to a maximum U(i). Correspondingly, the coefficients range

over a number of possible values (indicated by the subscript “level”), which weigh the levels ofchannel degradation. Given a specific link budget and a desired BER (i.e., the physical layer QoS) tobe kept, a finite set of values rlevel

(i ) , corresponding to coding and bit rates capable of coping with thepossible ranges of fade attenuation, can be computed (see [12] for details in a given instance of linkbudget).

2.2 Applicable network models

According to the information available to the master on the fading conditions of the traffic stations,two possible models can be applied: static or dynamic.

2.2.1. Static model. In this case (considered in detail in [12]), we suppose that no real-time measurement isavailable to the master station on the current attenuation caused by signal fading at the traffic stations, except fora binary information on the station’s status being either “clear sky” or “rain”. Thus, only “a priori” information,derived by long-term weather statistics, is taken into account. On the other hand, the traffic stations are assumedto locally measure their own fading levels, and to apply on-line their fade countermeasures. At the masterstation, to each value

†

rlevel(i ) of the data redundancy required by station i, a corresponding probability

†

plevel(i ) is associated. The associated probability values can be estimated [12] from the knowledge of the

traffic station’s geographic position, provided that the attenuation exceeded for a given percentage(0.01%) of an average year is available (typically, from long-term measurements), by deriving theattenuation for other percentage values from the ITU-R interpolation formula [13]. In this model thefading is not intended by the master as instantaneous, but it is described by the probability of a certainstation to be in a given range of fade values, owing to its geographical position. Finally, once theprobability distribution has been evaluated, it is straightforward to obtain the correspondingprobabilities conditioned to the rain event.

A number of weather forecast scenarios are then available, which can be used to compute an averageperformance indicator of the station.

2.2.2. Dynamic model. The master station is supposed to have a rather accurate knowledge of the levelof fading that is currently affecting each traffic station. This may be either the most recent value thatthe stations have communicated, or some function of the present and past values, representing an

4

“average” rough estimation of a fading class (fading levels can actually be predicted with a certainaccuracy over relatively short intervals [14], in the order of the second). In any case, the masterassumes the value in question to hold over a future period, over which the performance indexes to beused for the bandwidth allocation are evaluated. The length of this period, called superframe, can befixed or variable. If fixed, the reaction of the system to the fade changes may not properly reflect thedynamics of the events; if variable, the master decides to perform the reassignments according to anexplicit request by a traffic station. The situation is the same as in the static case, as regards thepossible finite set of values taken by the redundancy coefficients and their calculation from the linkbudget, given a BER requirement; however, the coefficient value is now a deterministic quantity,which is known with probability 1 over the next decision interval. All the necessary performanceindexes can be computed, without the need to average out over the possible scenarios. Again, trafficstations are assumed to measure fade attenuation frame-by-frame and to apply the bit and coding ratesrequired to keep the BER desired, with a possible information rate reduction, when necessary.

3. Traffic Models and Relevant Performance Indexes

3.1 Real-time trafficAs far as the real-time traffic is concerned we only consider guaranteed bandwidth synchronous Continuous BitRate (CBR) connections, each at a flow of B kbps, which must be reserved to guarantee the proper level ofquality of service. The traffic of each station i, i=1,…,N, is considered to be independent of the others.Exponential distributions are used both for the inter-arrival time and the service time, with the time variableassumed continuous. If

†

Nmax(i) is the maximum number of connections acceptable at station i, the call blocking

probability experienced, which is the quantity of interest for this type of traffic, is given by the well knownErlang B formula :

†

PB(i )(Nmax

(i) ) =r( i)( )N max

( i )

Nmax( i) !

r( i )( )nn!

n= 0

Nmax( i )

 (1)

where

†

r(i ) = l(i ) m(i ) is the traffic intensity [Erlang], for station i, being

†

l( i) [s-1] the arrival rate of the

connection requests, and

†

1 m( i) [s] the average duration of each connection.

3.2 Non real-time trafficAs far as the non real-time traffic is concerned, we suppose that it originates from datagram flows,which are fragmented into fixed-size data units (DU) before transmission on the satellite channel. Ateach station i, DUs are queued in a finite buffer of capacity Q(i) and, in this context, the quantity ofinterest is the packet loss probability (

†

Ploss) of the non-guaranteed traffic in the queue of station i. Inorder to derive an approximate evaluation of this quantity, we consider a discrete-time self-similartraffic model, which represents the superposition of source active periods (bursts), each with Pareto-distributed ‘on’ time t (

†

Pr t = l{ } = cl-a-1 ,1 <a < 2 ), where

†

a and c are the parameter of thediscrete Pareto distribution and its normalization constant, respectively. The detailed description of themodel can be found in [15, 16].

Let us define a reference time interval T, which we call a slot, to which we will refer all the relevantparameters of our queues. The slot also represents the minimum duration of a datagram burst and theburst length t is expressed as an integer number of slots. Let Bng be the peak generation rate of eachasynchronous source [bits/s], and L the number of bits in a DU payload. Then,

†

R = T (L /Bng)È ˘= TBng LÈ ˘ is the number of DUs generated by an active burst in a slot (

†

xÈ ˘ being the

smallest integer greater than or equal to x). The numbers of new datagram sources becoming active ineach slot are i.i.d. Poissonian with parameter

†

lng( i) . If

†

lburst( i) is the rate [bursts/s] of datagram burst

generation at station i, then

†

lng( i) = lburst

( i ) ⋅ T (2)

5

The overflow probability of the buffer dedicated to the asynchronous traffic can be asymptoticallybounded in Q(i), as described in [16]. Let

†

Cng(i ) be the capacity variable for the asynchronous traffic of

station i, expressed in [bits/s], and H the DU’s header length in bits; then we define

†

X (i ) =Cng

( i)

L + H⋅ TÍ

Î Í ˙

˚ ˙ as the same bandwidth expressed in DUs per slot. By taking into account the

above mentioned upper bound and letting

†

t m represent the average burst length in slots, the

†

Plossprobability at station i can be approximated as:

†

Ploss(i ) (X (i )) =

minc ⋅ lng

(i ) Ra

a ⋅ (a -1) ⋅ X (i) - lng( i ) Rt m( )

⋅ (Q( i ))-a+ 1, 1Ï Ì Ó

¸ ˝ ˛

if X ( i) > lng( i) Rt m

1 otherwise

Ï

Ì Ô

Ó Ô (3)

The traffic model we have adopted is just one among a number of possibilities. What we need is aquantity reflecting the dynamic behavior of the bulk traffic queues, to be contrasted with the blockingprobability of the guaranteed performance traffic. An alternative recent model that could also serve ourpurpose is the one proposed and analyzed in [17].

At this point, it is worth noting that the bandwidth allocated to the non-guaranteed traffic at station i attime frame t is actually a random variable, as it depends on the number

†

n( i)(t) of guaranteed trafficconnections in progress at station i at the same instant, and on the corresponding redundancy factor.This factor may generally perceived differently at the traffic stations and at the master station,respectively, especially if the time t is far from the beginning of the superframe it belongs to. Referringto traffic station i, we have

†

Cng(i) (t) = C (i)b level

(i ) (t) - B n( i) (t) (4)

where

†

C (i) is the total capacity allocated to station i, expressed in bits/s, and

†

blevel(i) (t) is the bandwidth

reduction factor, which is the inverse of the redundancy coefficient at time t. Thus, also the quantity

†

X (i ) should be assumed time-variant, as the non-guaranteed traffic always takes the residual bandwidthnot used, at any given instant, by the guaranteed traffic. The time index will be dropped where notexplicitly necessary.As

†

n( i)(t) can assume only discrete values from 0 to

†

Nmax( i) , as a consequence,

†

Cng(i )(t) only takes on

discrete values with certain probabilities, depending on the probability of having

†

n( i)(t) connectionsin progress at time t at station i. If we indicate by

†

X j(i ) the realization of the variable

†

X (i )(t) ,

corresponding to

†

n( i)(t) = j , and define D = (L+H)/T, we have:

†

X j(i ) =

C( i)blevel( i) (t) - jB

DÍ

Î Í Í

˙

˚ ˙ ˙ , j = 0,1,...Nmax

(i) (5)

and

†

Pr X (i )(t) = X j( i){ } = Pr n ( i)(t) = j{ } (6)

where

†

Pr n( i)(t) = j{ } is given by the stationary distribution of a

†

M / M / Nmax( i) /N max

(i ) queueing system.

We assume as an indication of the packet loss rate at station i the quantity defined in (3), averaged overthe number of guaranteed bandwidth connections; thus we have:

†

P loss(i) C( i)blevel

( i) (t),N max(i )( ) = Ploss

(i) (j= 0

N max( i )

 X j(i) ) ⋅ Pr n(i )(t) = j{ } . (7)

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4. The Time Scales

From the above discussion it results clear that we are treating a problem with 4 different time scales:

1. The longest time scale S, or superframe, over which the master keeps constant the allocationsgiven to the stations. S is the reallocation period, and it may be specified of fixed or variablelength. When the length is fixed, whatever event may happen during a superframe, such asnew station(s) entering/leaving the network, or explicit reallocation requests arriving, it will beanalyzed in the next superframe, and the allocations assigned continue to be valid till the endof the current superframe. If the length is variable, the occurrence of any of the previous citedevents triggers the recalculation of the allocations and the beginning of a new superframe. Inthis latter case, in the absence of particular events, S may last even until the master switchesoff. In both cases, however, S is a multiple of the time “frame”, with a minimum value of Sequal to a given number s of frames, in order to avoid too many oscillations.

2. The intermediate time scale E, or fade class lasting time, during which the fade level of astation i does remain in the same fade class, i.e., the measured fade value may change, but theredundancy applied to the data is always the same, because the current fade level is still in thesame range as the previous one. This time scale is constituted by a random number of frames.When the fade class changes in such a way that the current connections cannot be any longeraccommodated in the assigned bandwidth (or some pre-defined “safety margin” is exceeded),a rescheduling of the allocations is requested by the slave to the master, and a new thresholdvalue

†

Nmax(i) must be computed according to the new allocation which will be received. If S is

defined of variable length, in this case we may have S=E.

3. A shorter time scale t, or frame, i.e. a repetitive, fixed time interval during which each slavestation makes some operations, such as to check its fade level, and to transmit its data.

4. The shortest time scale w, or transmission window, i.e. the length of the transmission windowassigned by the master to the slave station inside a frame for transmitting its data bursts.

We give the following definitions:

†

rlevel(i ) (t) = redundancy factor by which data transmitted by station i in frame t must be multiplied. It

assumes that all data transmitted by station i in frame t have the same redundancy, whatever the link is.

†

Yh(i ) = set of links at station i belonging to fade class h.

†

rlevel(i ),h (t) = redundancy factor by which data transmitted by station i in frame t over links belonging to

the set

†

Yh(i ) must be multiplied. We recall that, for the time being, we assume that all links at the same

station belong to a single fade class, so that

†

rlevel(i ) (t) =

†

rlevel(i ),h (t) for some h.

†

rlevel(i ) (S) = redundancy factor, which the master assumes is used by traffic station i during the next

reallocation period, whatever the link is.

†

rlevel(i ),h (S) = redundancy factor by which data transmitted in superframe S by station i over links

belonging to

†

Yh(i ) must be multiplied.

Some remarks can be made in relation to the time scales of the model.

a) The bulk data loss probability depends on the current threshold

†

Nmax(i) and on the overall bandwidth

†

C (i) currently allocated to station i. As we have seen, even these quantities may be time-variant. Inparticular, at a time instant t,

†

Nmax(i) is determined by the number of streams, each requiring bandwidth

†

rlevel(i ) (t)B , which can be accommodated in the current value of

†

C (i) . Therefore,

†

Nmax(i) can change for

two reasons: i) a change in the fading class, which produces a variation in the code or bit rate, yieldinga new redundancy coefficient

†

rlevel(i ) (t) ; ii) a bandwidth reallocation, which assigns a different value of

†

C (i) to the station. In either case, the new value of

†

Nmax(i) only affects the local CAC decisions.

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Moreover, if variable length superframes are allowed, should the bandwidth

†

C (i) become insufficientto support the connections in progress (or even barely sufficient, but leaving no space to the bulk datatraffic), a reallocation would be requested to the master. The latter, in doing the calculations that leadto the new decision, implicitly assumes that the current values

†

rlevel(i ) (S) it attributes to the earth stations

would last forever, and uses stationary distributions in the performance indexes. This gives rise to a“receding-horizon” or “repetitive” control strategy, where the master actually sees a control period thatis shifting ahead in the future each time it makes a new decision. In practice, we are interested in aprediction, over a future time horizon, of the would-be situation corresponding to “freezing” thecurrent values of

†

rlevel(i ) (S) . As an extreme situation, in the static model, the master station completely

disregards the time-varying measured values, and assumes to be in the presence of random variablesthat reflect an “average” behaviour.

b) In writing (7), we have exploited the fact that the time scales of the guaranteed and non-guaranteedtraffic are widely different, in order to use independent stationary distributions for both traffics. Inother words, the guaranteed traffic process is supposed to be quasi-stationary in computing (3), and thenon-guaranteed traffic queue is supposed to reach steady-state between successive jumps in theMarkov chain of the former [5, 18].

5. Control Architecture

As we already mentioned, our control architecture is essentially hierarchical in nature. Basically, thetraffic stations exert control actions on a short- and medium-term time scale, by deciding on theamount of redundancy to be applied to the data in transmission, and on the admission control of theirown connection requests, within a bandwidth temporarily assigned to the station by the master. Thelatter plays the role of a coordinator in the hierarchical setting, by dividing the total availablebandwidth among the traffic stations. Let us see now what happens on each of the four temporal timescales previously described and depicted in Fig. 1, as an example of variable length superframe, withS=E.

Superframe S1 Superframe S2 Superframe S3

E1(fade class 1) E2 (fade class 2) E1 (fade class 1) E3 (fade class 4)

fl1 fl2 fl2 fl3 fl3 fl4 fl4 fl5 fl4 fl4 fl6 fl4 fl5 fl7 fl7 fl…..

frame t transmission window w shadowed

Fig. 1. The four temporal time scales .

i) First level (on the longest time scale S):At each convenience, each station i sends the master the mean traffic intensity

†

r(i) , as well as

†

lng(i)

and

†

t m , for real-time and best effort traffic, respectively, together with the last redundancy

parameters

†

rlevel(i ) (t) , i=1, 2,...N. More generally, values

†

r(i),h ,

†

lng(i),h and

†

rlevel(i ),h (t) , h=1, 2,...,

†

Yh( i) ,

would be needed, for each individual link that connects the station to a specific destination (per linkvalues) . Taking into account the last updated value, at the (fixed or variable) superframe time themaster computes the bandwidth to be allocated to each station, according to some criterion, e.g., byperforming a proportional assignment, based on the amounts of requested bandwidth, or byminimizing a cost function, which takes into account a global (system-wide) performance index,reflecting blocking and loss probabilities. According to the policy adopted, the master computes the

8

capacity to be assigned to each single station, and sends the capacity values to the traffic stations ina reference burst, transmitted at the beginning of each superframe (superframe reference burst,SRB). The capacity

†

C (i) assigned to station i remains unaltered for the whole superframe duration.The bandwidth allocation should take into account continuation of outstanding connections as aconstraint on the minimum possible assignment to a given earth station. Moreover, traffic stationsare allowed to file requests for bandwidth re-allocation asynchronously. As we have alreadymentioned, a possible triggering event for a re-allocation request may be the attainment of asituation where no residual bandwidth is available for best-effort traffic or, more generally, a“safety margin” is exceeded in the bandwidth occupied by the ongoing synchronous connections(pre-outage situation).As an alternative, the master may perform a centralized high level call admission control by usingsystem-wide information (system-wide call admission control, SW-CAC). In this case, it isnecessary to know the disaggregated traffic intensities per link, the calculation of the blockingprobabilities requires the use of a stochastic knapsack model [3], and there is a separate buffer forthe best-effort traffic of each fading class at each station. This case is not investigated in this work.

ii) Second level (on the time scale E):At each change of fade class within the received capacity partition

†

C (i) , the station computes itsown threshold (or region in the space of connections) for local call admission control, by ideallyoperating in a “receding-horizon” mode, i.e., by assuming that the measured values will holdforever, and re-computing the threshold with the same criterion, at each fade class change. In doingthis, two situations may take place: either there a single fade class present at the station (whichimplies that the call blocking probability is computed from an Erlang-B function), or there are twoor more, effectively resulting in different bandwidth requirements per call groups. The latterimplies the use of a stochastic knapsack model [3] in the calculation, and a correspondinglydifferent expression of the residual bandwidth for best-effort traffic, unless the bandwidthpartitioning is extended to the fading classes. In this case it is also necessary to know thedisaggregated traffic intensities per link, and to use a separate buffer for the best effort traffic ofeach different fade class.

iii) Third level (on the time scale t):Every frame time t, each station i measures its attenuation level(s) and verifies the class of fade.Each station classifies each “link” it maintains to any other station within the appropriate fadeclass. The time interval E is generally longer than t.At the beginning of each frame t each station receives a frame reference burst (FRB), transmittedby the master, which is a copy of the SRB as far as the allocations are concerned, and containsupdated values relevant to the fades of all stations, as well.

iv) Fourth level (on the shortest time scale w within the frame t):By using the same measured attenuation value(s) and the ensuing classification andredundancy(ies), each station transmits its data frame by frame in its own transmission window,according to the received transmission time plan. Piggybacked with the data, each station sends themaster the information on the fade level measured in the current frame t. This information will beredistributed by the master within the FRB. The latter operation is necessary to allow theevaluation of the link-by-link fade classes.

6. Hierarchical Control: Dynamic Case

We give now a specification of control goals, actions and algorithms in the dynamic case. The staticcase has been studied in [12]. For the sake of notational simplicity, we suppose to have only one fadingclass at a time per station. We start with the local (traffic earth station) level.

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6.1. Control level at the traffic earth station (local level)

The lower control level used in the dynamic case is the same as in the static case. We adopt a strategywhose goal is to satisfy a constraint on the blocking probability, given the bandwidth assigned to thestation.

Then, if we want that

†

PB(i ) £ h( i )

, we should compute the minimum bandwidth requirement for theguaranteed bandwidth, real-time traffic

†

Crt(i) =

Y (i) min Y (i) :PB

(i) Y (i) B rlevel( i) (t)( )Í

Î Í ˙ ˚ ˙

Ê Ë Á ˆ

¯ ˜ £ h(i)Ï

Ì Ó

¸ ˝ ˛

(8)

and, consequently, the maximum number of connections allowable

†

Nmax(i) C(i)( ) =

Crt( i) (B rlevel

(i) (t))Î ˚ if C rt(i) < C (i)

(C( i) (B rlevel(i ) (t))Î ˚ if C rt

(i) ≥ C (i)

Ï

Ì Ô

Ó Ô (9)

†

rlevel(i ) (t) being the redundancy factor that is taken into account at the time of the calculation. Expression

(9) can be modified to include a minimum bandwidth

†

Bd( i)

, guaranteed for datagram traffic. The current

value of

†

Nmax( i) is used by the station to perform admission control.

6.2. Control level at the master station (high level)

The master’s coordination strategy is here described, still in the situation of a single fading class perstation. We recall that the master station uses the value

†

rlevel(i ) (S) or, correspondingly,

†

blevel(i) (S) , in its

calculations. Actually, this value may change during a superframe, whenever a reallocation, triggeredby some request, takes place. For the sake of notational simplicity, we will continue to use the samenotation (indexed only by the superframe) throughout.

The cost function is essentially the same as in the static case [12]. The rationale behind it is to set apenalty on bandwidth assignments that would push the partition for real time traffic at each stationbelow the minimum necessary to satisfy the threshold condition on the blocking probability. Forbandwidth assignments that respect this constraint, the loss probability of best-effort traffic is taken asa cost. However, unlikely the situation considered in [12], where the actual values of the redundancyfactors are unknown, and the cost function is averaged over their probability distribution, we use theirmeasured values in the evaluation of the cost. We have now:

†

J(i )(Z(i )) =P loss

(i ) Z(i )blevel(i ) (S),N max,master

(i) Z(i )( )[ ] if Z ( i) ≥ Crt,master( i)

Q if Z (i) < C rt,master(i)

Ï Ì Ô

Ó Ô (10)

where

†

Z (i) represents the capacity variable and

†

Q is a sufficiently large number (a value of 10 is sufficient inmost cases). Moreover,

†

Crt ,master(i) =

Y ( i ) min Y (i) :PB

(i) Y ( i) B rlevel(i ) (S)( )Í

Î Í ˙ ˚ ˙

Ê Ë Á ˆ

¯ ˜ £ h( i)Ï

Ì Ó

¸ ˝ ˛

(11)

and

†

Nmax, master(i) =

Crt,master(i ) (B rlevel

( i) (S))Î ˚ if C rt,master(i ) < Z(i)

(Z (i ) (Brlevel( i) (S))Î ˚ if C rt,master

(i) ≥ Z(i )

Ï

Ì Ô

Ó Ô (12)

The goal is then to minimize

10

†

J(Z (1),Z (2) ,..., Z( N) ) = J(k ) Z( k)( )k= 1

N

 (13)

subject to the “static” and “dynamic” constraints

†

Z( j)

j=1

N

 = C

Z( i) £ CcZ( i) ≥ n (i) (S)rlevel

(i) (S) B

Ï

Ì

Ô Ô Ô

Ó

Ô Ô Ô

†

i = 1,...N (14)

where

†

Cc is the maximum allowable information rate for each carrier. The third constraint in (14)stems from the willingness to guarantee the continuation of all connections in progress. The problem

admits the solution

†

C (i) = Zopt(i ) ,

†

i = 1,...N , if

†

Crt,master( j)

j= 1

N

 < C ; otherwise, the allocation is calculated as

†

C (i) = min C Crt ,master

(i)

Crt,master( j)

j=1

N

Â, Cc

Ï

Ì

Ô Ô Ô

Ó

Ô Ô Ô

¸

˝

Ô Ô Ô

˛

Ô Ô Ô

(15)

Also relations (10)-(15) can be modified to include a minimum bandwidth

†

Bd( i)

guaranteed for

datagram traffic. In the bandwidth assignment we suppose that variables

†

Z(i) can assume discretevalues that are integer multiples of a minimum bandwidth unit (mbu). The minimization of (13), withrespect to discrete variables

†

Z(i) , can be efficiently effected by means of a dynamic programmingalgorithm, following the procedure outlined in [3]. Some modifications are required to take intoaccount the inequality constraints in (14).

7. Dynamic Case Numerical Results

The results relevant to the static case can be found in [12]; in this Section, only the results relevant tothe dynamic case are presented.The simulation refers to a fully meshed satellite network described in Section 2. In Table I the mostsignificant parameters of the MF-TDMA system are reported. The values needed to compute the linkbudget are relevant to the transponder #1 of the Italsat national coverage payload, which operated inthe 20/30 GHz band [19]. The information rate of 6.554 Mbps for each carrier is obtained with a 4/5punctured convolutional encoder. The value of 7 dB of channel Eb / N0 (bit energy to one-sided noise

spectral density ratio), after 1 dB of modem implementation margin, is assumed as the threshold of theclear sky conditions. At the threshold conditions, after the Viterbi decoder [2], the bit error rate is 10-7.In order to compute the resulting net values of Eb / N0 at the earth station’s receiver input, relation

(16) is given below. No automatic gain control feature operates on the transponder. For this reason theattenuation on the up-link affects both the up- and down-link signal to noise values.

Eb / N0 = C(res ) -10Log10br - mi (16)where:

C (res) = Cr(up) - Aup

+ Cr(dn) - Au p

- Ad -10Log10 10(Cr( up) - Aup ) / 10

+10(Cr(dn ) - Aup - Ad ) / 10Ê

Ë ˆ ¯

is the resulting

†

C / N0 (carrier power to one-sided noise spectral density ratio) at the earth stationreceiver,

†

Cr(up) is the reference (in clear sky) up-link

†

C / N0 = 80.7 [dBs-1],

11

†

Cr(dn) is the reference (in clear sky) down-link

†

C / N0= 81.6 [dBs-1],

†

Ad is the dB down-link attenuation of the receiving station,

†

Aup is the dB up-link attenuation of the transmitting station, after up-link power control

intervention:

†

Aup= 0 , if the up-link attenuation

†

Au £ pr (

†

pr is the up-link power control range = 5 dB);

†

Aup= Au - pr , if

†

Au > pr ,

†

br is the data bit rate in bit/s

†

mi is the modem implementation margin (assumed equal to 1 dB).

Stations’ antenna diameter 1.8 mStations’ power 13 dBWSatellite G/T 5.9 dB/˚KSatellite E.I.R.P. (Effective Isotropic Radiation Power) 48 dB WNumber of carriers 3Capacity of each carrier (QPSK modulation) 8.192 MbpsUp-link power control range 5 dBMinimum net Eb / N0 in clear sky conditions 7 dB

Bit error rate (BER) guaranteed 10-7

Possible data coding rates (convolutional) 4/5 (clear sky), 2/3, 1/2Total information bit rate in clear sky conditions 19.66 MbpsTotal information bit rate of the system in clear skyconditions after system overhead

18 Mbps

Maximum allowable information bit rate per carrier

†

Cc 6 Mbps

Table I. Most significant values of the MF-TDMA system, considering the Italsat satellite.

Table II contains the fade classes of the traffic stations, which depend on

†

C / N0 values. Each fadeclass imposes the adoption of the indicated transmission parameters (and then

†

rlevel values; thesuperscript (i) has been omitted, as they are the same for all stations) to limit the BER below thechosen threshold of 10-7.

Fadeclasses

†

C / N0 [dB]

†

rlevel

†

blevel coding rate, bitrate [Mbps]

Net

†

Eb /N 0

1 >77.13 1 1 4/5, 8.192 7 dB 2 74.63-77.13 1.2 0.8333 2/3, 8.192 4.5 dB 3 72.63-74.63 1.6 0.625 1/2, 8.192 2.5 dB 4 69.63-72.63 3.2 0.3125 1/2, 4.096 2.5 dB 5 66.63-69.63 6.4 0.15625 1/2, 2.048 2.5 dB 6 < 66.63 - - outage -

Table II. Redundancy factor rlevel (and blevel ) versus fade classes.

The situation investigated shows two faded stations (number 1 and number 4) out of ten active ones.Seven of the stations that are in clear sky send data to stations in clear sky as well. Station 2 sends datato station number 1, and therefore experiences fading on the down-link. Station number 4 sends data tostation number 1, and thus these data experience fade on both up- and down-link. Station number 1sends data to a station that is in clear sky; thus, these data are affected by up-link attenuation only.The attenuation data are taken from a data set chosen from the results of the propagation experiment,in Ka band, carried out on the Olympus satellite by the CSTS (Centro Studi sulle TelecomunicazioniSpaziali) Institute, on behalf of the Italian Space Agency (ASI). The up-link (30 GHz) and down-link(20 GHz) samples considered were 1-second averages, expressed in dB, of the signal power

12

attenuation with respect to clear sky conditions. The attenuation samples were recorded at the Spinod’Adda (North of Italy) station, in September 1992. The fade situation at station 4 has been simulatedby shifting in time the up-link fade of station 1 and the down-link fade of station 2, and by assumingthat at station 4 the two fade events occurred simultaneously.

The simulative analysis reported in the following is the result of the dynamic adaptive strategy, basedon real-life fading attenuation samples. The attenuation level determines, according to (16) and TableII, the attribution of a station to a certain fade class. The data reported in Table III have been used forthe generation of the traffic.

All stations are loaded with the same traffic intensity, both stream and datagram. The minimumbandwidth unit (mbu) that can be allocated has been taken equal to 32 kbps. The stream source rate (B)is assumed to be 64 kbps. No spare bandwidth is guaranteed for datagram traffic (

†

Bd(i ) = 0 for " i ). The

synchronous reallocation interval is 1800 s. The simulation program has been structured in twomodules, working in cascade. In the first one, the synchronous traffic is generated, along with thefading trace; all bandwidth allocations and call acceptance thresholds are computed, and the ensuingblocking probabilities are evaluated. Moreover, the envelope of the residual bandwidth forasynchronous traffic versus time is stored, to be used as input to the second module. This latter, whosetask is that of simulating the asynchronous traffic, evaluates the loss probabilities at each station’squeue, whose service time is determined by the observed residual bandwidth.

Stream connections generation rate

†

ls =0.05 calls/s

Average stream connection duration

†

1/m=120 sMaximum call blocking probability

†

h=5%

Shape parameter of the Pareto distribution

†

a =1.5Average datagram burst duration

†

t m=1.945 s

Datagram peak bandwidth 512 kbpsDatagram reference time slot 1 sDatagram burst intensity

†

lburst =0.25 burst/sData Unit (DU) size 384+40 bitsBuffer dimension [DUs] 8000

Table III. Data used in the simulation.

Three different strategies are considered, as regards the reallocation timings. In the first one thebandwidth reallocation is performed synchronously, at the beginning of each fixed length superframeS, while in the second one the bandwidth is reallocated on request of any station that cannot afford afade level variation or an increment in the average traffic offered (variable length superframe). Therequest is triggered by insufficient capacity to continue carrying all connections in progress. The thirdstrategy considers both events for making a reallocation. In Fig. 2 the call blocking and the cell lossprobabilities are shown for all 10 stations and for the three different strategies. Each simulation rungives values averaged over a 100,000 s time span (minus 10,000 s to cut the initial transient); the finalvalues are obtained by averaging the results of a number of simulation runs sufficient to produce a 5%confidence interval at 95% level. We can see that the third strategy gives the best results; in fact it isthe only one that allows to keep the call blocking probably below the pre-fixed threshold of 5%,without a significant increment in the cell loss probability, even at the faded stations. Furthermore, itcan be observed that the combined strategy yields a more balanced distribution of both probabilitiesamong the stations. These results are explained by the behaviour of the three strategies versus time,shown in Fig. 3. The figure refers to an observation window of 20,000 s, over which the total allocatedbandwidth and the residual bandwidth for datagram at station number 4 are shown. The synchronousallocation is not able to follow the rapid fade changes, thus giving rise to non-negligible periods whereno capacity is available for datagram. On the other hand, the reallocation on request, used alone, doesnot release the excess of bandwidth obtained to overcome the fade events, thus starving the otherstations. The adoption of both methods, instead, solves all drawbacks and gives appreciable results, as

13

shown in Fig. 4, where the call blocking and data loss probabilities of the entire system, averaged overall stations, are lower in the case where the combined strategy is used.

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

1 2 3 4 5 6 7 8 9 10

Station number

Combined

Allocation on request

Synchronous allocation

(a)

1E-05

0.0001

0.001

0.01

0.1

1 2 3 4 5 6 7 8 9 10

Station Number

Combined

Allocation on request

Synchronous allocation

(b)

Fig. 2. Call blocking (a) and DU loss probabilities (b) at each station.

14

-1

-0.5

0

0.5

1

blevel

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0

1800

3600

5400

7200

9000

1080

0

1260

0

1440

0

1620

0

1800

0

1980

0

Time [s]

residual bandwidth for datagram

total allocated bandwidth

blevel

Station # 4

(a)

-1

0

1

blevel

0

2000

4000

6000

8000

10000

12000

14000

0

1800

3600

5400

7200

9000

1080

0

1260

0

1440

0

1620

0

1800

0

1980

0

Time [s]

Station # 4

total allocated bandwidth

residual bandwidth for datagram

blevel

(b)

15

0

1

blevel

0

2000

4000

6000

8000

10000

12000

0

1800

3600

5400

7200

9000

1080

0

1260

0

1440

0

1620

0

1800

0

1980

0

Time [s]

total allocated bandwidth

blevel

residual bandwidth for datagram

Station # 4

(c)

Fig. 3. Synchronous allocation (a), allocation on demand (b), and both allocation strategies (c)behaviours at the station number 4. The total bandwidth allocated, the residual bandwidth fordatagram and the parameter blevel are shown for the three different cases as functions of time over a

20,000 s observation window.

0

0.01

0.02

0.03

0.04

1 2 3Synchronous Allocation

Ploss

Pblock

Allocation onRequest

Combined

Fig. 4. Call blocking and DU loss probabilities of the entire system for the three strategies.

8. Conclusions and Future Work

The combination of a BER-related fade countermeasure technique with a bandwidth allocation andCAC scheme has been investigated, in the context of a geostationary satellite network, operating in Ka

16

band. The resulting control architecture spans the physical, the MAC, and the network layers,considering in each of them the relevant QoS constraints. The control task has been decomposed in ahierarchical setting, where different strategies for the decisions taken by the master station have beencompared. The comparison demonstrated that the combination of periodic (synchronous) and event-driven (asynchronous) decisions on the bandwidth allocation gives the best results in terms of callblocking and data loss probabilities. One limit of the current system is that the master performs anyreallocation at the beginning of a superframe, by solving a discrete optimization problem, whosecomputational time imposes a minimum on the superframe length. This minimum may not becompatible with the frequency of the reallocation requests coming from the earth stations.The work done opens the way for further interesting investigations. A first interesting point regards thedistribution of the optimization task among the traffic stations or, at the opposite extreme, thecentralization of the CAC for the whole system at the master station, in a “complete sharing” [3]fashion. In fact, there is a whole range of possible control architectures that can be investigated, andthe one considered in this paper is an intermediate case of hierarchical coordination. In particular, it isworth noting that there is a form of looser coordination, which gives more autonomy to the localcontrollers, though still keeping a role for the master in the bandwidth assignment. In this case, theearth stations, rather than communicating their fade and traffic parameters to the master (as in thehierarchical setting described in this paper), independently compute the bandwidth they would need tosatisfy their requirements. This computation is done in terms of performance indexes (consisting, forinstance, of the satisfaction of given upper bounds on blocking and loss probabilities), starting from aninitial bandwidth assignment, which is provisionally used to perform the CAC operation. Thebandwidth that is necessary may be greater or lower than the temporarily assigned one. The trafficstations communicate their bandwidth requirements to the master, which, on the basis of all requests,performs a redistribution of the total bandwidth. The new value is taken by the earth stations both tocompute a new admission control strategy and to restart the bandwidth calculation. In this setting, themaster’s assignment algorithm could be based on some simpler allocation strategies (e.g., allocationproportional to the bandwidth requested by the earth stations). This type of coordination policy is thesubject of forthcoming work.Other aspects to be further developed are the following: i) the introduction of explicit constraints onthe minimum and maximum allowable assignments in the dynamic programming algorithm used bythe master station; ii) the adoption of on-line gradient descent techniques, of the type considered in[20], to relax the discrete integer optimization problem to a continuous one, whose solution can bespread over time, instead of being concentrated at the beginning of the superframe interval. Both pointsi) and ii) above address the problem of reducing the master’s computational time for the bandwidthallocation.

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