Modeling epidemic data diffusion for wireless...

WIRELESS COMMUNICATIONS AND MOBILE COMPUTINGWirel. Commun. Mob. Comput. (2012)

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.2233

RESEARCH ARTICLE

Modeling epidemic data diffusion for wirelessmobile networksMohammad Towhidul Islam1, Mursalin Akon1, Atef Abdrabou2 andXuemin (Sherman) Shen1*

1 Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G12 Department of Electrical and Computer Engineering, United Arab Emirates University, Al-Ain, Abu Dhabi, UAE 17555

ABSTRACT

Data/content dissemination among the mobile devices is the fundamental building block for all the applications in wire-less mobile collaborative computing, known as mobile peer-to-peer. Different parameters such as node density, schedulingamong neighboring nodes, mobility pattern, and node speed have a tremendous impact on data diffusion in a mobilepeer-to-peer environment. In this paper, we develop analytical models for object diffusion time/delay in a wireless mobilenetwork to apprehend the complex interrelationship among these different parameters. In the analysis, we calculate theprobabilities of transmitting a single object from one node to multiple nodes using the epidemic model of spread of dis-ease. We also incorporate the impact of node mobility, radio range, and node density in the networks into the analysis.Utilizing these transition probabilities, we estimate the expected delay for diffusing an object to the entire network bothfor single object and multiple object scenarios. We then calculate the transmission probabilities of multiple objects amongthe nodes in the wireless mobile network considering network dynamics. Through extensive simulations, we demonstratethat the proposed scheme is efficient for data diffusion in the wireless mobile network. Copyright © 2012 John Wiley &Sons, Ltd.

KEYWORDS

mobile P2P; data dissemination; wireless data diffusion

*Correspondence

Xuemin (Sherman) Shen, Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, CanadaN2L 3G1.E-mail: [email protected]

1. INTRODUCTION

The multifaceted utilization of mobile computing devices,including smart phones, personal digital assistants,tablet computers with increasing functionalities, and theadvances in wireless technologies, has fueled the uti-lization of collaborative computing (P2P, peer-to-peer)technique in mobile environment. Cheap and ubiquitousplatforms of networked mobile devices will be the key toreal-time delivery of large volumes of useful informationand would support a variety of applications. Mobile collab-orative computing, known as mobile peer-to-peer (MP2P),can provide an economic way of data access among usersof diversified applications in our daily life (exchangingtraffic condition in a busy high way, sharing price-sensitivefinancial information, getting the most-recent news), innational security (exchanging information and collaborat-ing to uproot a terror network, communicating in a hostile

battle field), and in natural catastrophe (seamless rescueoperation in a collapsed and disaster torn area).

Wireless mobile devices often form on-demand oropportunistic networks to disseminate or exchange dataamong themselves. The opportunistic network has charac-teristics of prolonged disconnection and unpredictable andunstable topologies. Therefore, the continuous multihopconnection between two end point devices is a fairy talein most of the cases. The network and application protocolshould exploit the proximity of mobile devices to bridgepartitions of end point devices.

The great success of P2P networks in wired environ-ments inspires the evolution of MP2P networks. MP2Phas been proposed to share the network resources amongthe peers in mobile network [1]. In a MP2P network,a set of moving peers (throughout the paper, the termpeer, mobile device, user, and node are used inter-changeably) collaborate with each other to exchange

Copyright © 2012 John Wiley & Sons, Ltd.

Modeling epidemic data diffusion for wireless mobile networks M. T. Islam et al.

information without using any central coordination orfixed infrastructure in a mobile environment [2–4]. In thisparadigm, peer devices are those in transmission range,directly connected with each other in a pairwise basis. Tocommunicate with peers who are outside of transmissionrange of a node, messages are propagated through multiplehops. MP2P can be implemented in many kinds of networkconnectivity and mobility conditions.

In many applications, it is necessary to disseminateinformation to the entire network, that is, to all the par-ticipating peers, as fast as possible, because of the tempo-ral nature of the information. Because the transmission ina wireless network is broadcasting in general, we deviseanalytical models for data diffusion using the broadcastproperty of the wireless nodes. When multiple nodes tryto broadcast data simultaneously, there will be contentionamong the nodes. In many cases, nodes in contending radiorange maintains a scheduling for distributing data. In ourmodels, we also incorporate the interleaving data transmis-sion among the contending nodes. Mobility is a key factorfor data dissemination in a mobile network. To address themobility effect on data diffusion, we consider the speed ofnodes and their pattern of movement. Hence, we developgeneralized analytical models for epidemic data diffusionin a mobile network, both for single object and multipleobjects diffusion. To the best our knowledge, these arethe first analytical models in epidemic data diffusion formobile network.

The remainder of the paper is organized as follows.In Section 2, we give a brief description of existingresearch works in analytical modeling on data dissemina-tion. In Section 3.1, we describe the system model, and inSection 3, we describe our analytical model for data dis-semination based on epidemiology and probability, respec-tively. Extensive simulations are performed to verify ourmodel in Section 4. We finalize our discussion in Section 5.

2. BACKGROUND ANDRELATED WORK

Researchers have been actively investigating data dissem-ination method for mobile networks, especially mobile adhoc networks [5–9]. As a result, several data disseminationtechniques have been proposed in the literature. Most ofthe technique relies on the simulation results for the ver-ification of their system. A few of the works provide theanalytical model for the data dissemination.

Epidemic model for disease dissemination is an impor-tant research topic in biostatistics and physiology. Thespreading of epidemics is analogous to data diffusion pro-cess in many scenarios of communication network. Thecommunication researcher has recently utilized the epi-demic model of disease spreading in the field data dis-semination for ad hoc network. The mathematical fieldof epidemic modeling has a long history where both thestochastic and deterministic models are used to study forinfectious disease [10,11].

Reed-Frost [12] model is the most referenced work inthe field of mathematical analysis of epidemiology. How-ever, this model lacks of generalization for generatingfunction. Later, Deitz et al. provided a modified modelof En’ko, which eliminates the generalization problem ofReed-Frost model [10].

Maria et al., propose seven degrees of separation systemfor information exchange between mobile and stationarynodes in P2P fashion [13]. This system exploits the hostmobility and spatial locality of information. The authorsutilize stochastic epidemic model to analytically determinethe delay for data spreading to all devices in a network.Their model is a pure birth process that is simple contin-uous time Markov chain (CTMC). Because only a smallnumber of nodes are considered in this analysis, there isa need of rigorous experiment with many nodes to vali-date the system. A similar work is presented by Helgasonet al. [14]. The authors suggest cooperative wireless con-tent distribution using CTMC. The cooperation among thenodes is categorized in three basic types: no cooperationat all, cooperative sharing, and generous sharing. In coop-erative sharing, a node shares only the contents that theyare interested, whereas in generous sharing, a node relaysthe content of other nodes. They also extend their modelto capture energy and storage limitation of mobile devices.They calculated the absorption state of CTMC numerically.Their numerical results showed that generous cooperationmodel diffuses data quicker than any other model. How-ever, an analytical study of the Markov chain model isquite complex even for simple epidemic model of datadiffusion. Moreover, numerical solutions of such a modelbecome impractical when the number of nodes is enor-mous. On the other hand, we are interested in modelingdata dissemination in large-scale networks.

Recently, modeling based on ordinary differential equa-tion (ODE) for epidemic style data dissemination is gain-ing popularity in the literature [15,16]. The ODE modelsappear as fluid limits of Markovian models with appropri-ate scaling when the number of nodes under considerationis large. The major disadvantage of ODE models over theMarkovian model is that they provide the moments of thevarious performance metrics of interest whereas a numeri-cal solution of Markov chain models can provide completeinformation about coverage and replication of data.

Khelil et al. develop an epidemic-based diffusion algo-rithm using simulation results [17]. The simulation resulthas revealed the impact of node density on information dif-fusion in a mobile network. The observation has guidedthe authors to lay out an ODE to model the data diffu-sion pattern. Our analytical model is different from thismodel because our model is extended to incorporate theother network dynamics for information diffusion.

In [18], Mundinger et al. present a data disseminationsolution for nodes with different download and uploadcapacity. The solution based on differential download andupload capacity provides the lower bound for data dissem-ination among nodes in mobile network. In this paper, theauthors has utilized simulation data to measure both the

Wirel. Commun. Mob. Comput. (2012) © 2012 John Wiley & Sons, Ltd.DOI: 10.1002/wcm

M. T. Islam et al. Modeling epidemic data diffusion for wireless mobile networks

upload and download capacities. Therefore, this analyticalsolution is heavily dependent on the simulation data insteadof real life scenario.

Recently, Özkasap et al. have presented the exact perfor-mance analysis of the data dissemination in P2P networkusing anti-entropy algorithm [19,20]. Their data distribu-tion policy is almost similar to epidemic format of datadistribution. They describe three different ways of datadistribution: push, pull, and hybrid. In push approach,the sender proactively asks and delivers objects to thereceiver. In pull method, the receiver queries the requiredobjects from the sender and acquires the objects. Thehybrid system is a simple combination of both push andpull approaches. The paper claims the exact performancemeasure in P2P epidemic information diffusion. This epi-demic style information dissemination protocol cannot beapplicable in MP2P because this protocol does not con-sider the churn out of peers, which is a common phenom-ena in MP2P network. Our proposed scheme considersthe mobility and uncertainty in mobile P2P network thatstand out our scheme from this push, pull, and hybrid datadissemination.

Gossip style data exchange is an important area ofresearch for data dissemination in large-scale data distri-bution. Rena et al. have presented a probabilistic analysisof push/pull approach of a gossip-based protocol [21]. Thegossip style data dissemination protocol has been devisedfrom the analytical model using the transition probabili-ties of the nodes inside a network. The nodes change theirstate by acquiring, keeping, and releasing objects duringdata dissemination operation. They have investigated thereplication and coverage of an object in a large-scale dis-tributed system. This investigation helps to formulate theexpression of approximate time and amount or replicationof an object in terms of the number of nodes in a system.The optimal buffer size for each node to maximize theperformance of data dissemination in gossip style is oneof the contributions of this work. Our proposed schemediffers with this data dissemination protocol in terms ofapplication domain because it is most suitable for wirelessmobile network.

3. MODELING AND ANALYSIS OFEPIDEMIC DATA DIFFUSION

In this section, we first describe the system model forthe problem domain. Subsequently, we identify and modelanalytically the data diffusion process in wireless mobilenetwork using MP2P. We separately analyze two differ-ent scenarios. First, we consider a situation, where a singleobject needs to be distributed to all the interested nodes inwireless mobile network. Second, we consider every nodein the network holds multiple objects, and these objectswill be distributed to every other nodes in network. In otherwords, there are multiple objects prevail in the network,and a node is interested in all the objects. Eventually, eachnode will acquire all the objects present in the network. We

discuss two analytical models, one for each scenario, in theSections 3.2 and 3.3, respectively.

3.1. System model

In our system model, we consider a network of mobilenodes, interested in exchanging information. We assumethat these nodes can form a network on-the-fly using anad hoc networking technology to establish communicationbetween them. Although search for hardware technolo-gies to engineer ad hoc networks is still an active area ofresearch, several of them have already been implementedin wireless local area network [22] and are intended to beimplemented in future cellular networks [23–25]. In ourmodel, each node participates in forming a P2P network.We assume that the network is equipped with a low-level(lower than application level) single-hop broadcast service.We consider that all nodes communicate in half-duplexmode. While a node is active in the network, it can discoverall other nodes within its radio range and exchange infor-mation with them. In the rest of the paper, we emphasizereliable communication at the application level, withoutconsidering lower level details. Figure 1 shows an exampleof the considered network. In the figure, the circles outsidethe wireless gateway and the mobile devices show the radiorange of the gateways and devices. The overlapping circlesdenote the connection between the devices. The arrows indifferent direction attached with the users represent direc-tion of movement of the users. These mobile nodes receiveinformation or data as object from either public or pri-vate networks and from user inputs. We consider that eachmobile node is equipped with (primary, secondary, or bothkinds of) memory, as large as to store all the objects. Weconsider all objects to be diffused to the entire network.Each of the nodes can transmit a complete object with sin-gle transmission. This is also true for reception of data.The transmission and reception operations are consideredas atomic and error free.

3.2. Single object diffusion

Let the number of peers in the P2P network be N andthe peers be designated as n1; n2; : : :; nN . These nodesare moving in a closed area of size A with random direc-tion mobility (RDM) model [26]. The transmission rangeof each node is r. Let, at any moment t , the total number ofnodes infected with a specified content/object be Ct . Thereare N � Ct susceptible nodes in the network, and all ofthem are interested to have the particular object. Let St bethe number of susceptible nodes in a t th period. Formally,the relation of the infective, susceptible, and total nodescan be expressed as

Ct C St DN; 8t (1)

Therefore, this system can be categorized as a demand-based system [27]. In epidemic modeling, a healthy person



Figure 1. Schematic diagram of the network model.

becomes infected by the transportable disease when hemeets an infected individual. Even multiple persons canbe infected at the same time. To resemble the real-lifescenario of broadcast, we consider that an infected nodecan transmit data to multiple susceptible nodes in a singletransmission.

Consider that the total number of new infected nodes inthe tC1th time is C 0tC1. Therefore, the total infected nodesin the t C 1th time is

CtC1 D Ct CC0tC1 (2)

If an infected node has k neighbors, the probability thatany of the neighbors is susceptible can be derived as

˛ DSt

N � 1(3)

We also consider two facts of wireless mobile network:mobility and transmission error due to contention. In amobile network, the nodes are not stationary. Instead, theyare moving in a different direction. Therefore, we need toidentify the meeting probability between nodes in a net-work. Additionally, in the wireless network, multiple nodesare able to transmit concurrently. When a node obtains datafrom multiple nodes simultaneously in a wireless environ-ment, none of the data is correct because of reception error.Therefore, it is not guaranteed that the contact between aninfected and susceptible nodes generates a successful eventof content transmission. Let ˇ be the meeting probability oftwo nodes in a network and � be the probability of success-ful exchange of data between interested peer in a wireless

mobile network. Therefore, a susceptible will be convertedto an infective with the probability

p D ˛ � ˇ � � (4)

The nodes in the mobile network infected with objectsindependently. The independence of the infection eventsmotivates us to model the demand-based data diffusion inthe wireless mobile network with chain-binomial model. Inthe chain-binomial model, the number of susceptible nodethat will be infected in the next time cycle follows the bino-mial distribution with parameter St , p. Thus, the one-steptransition probability of the entire system is

Pij ŒCtC1 D jC i jCt D i �D

St

j

!.p/j .1� p/St�j

D

N� i

j

!.p/j .1� p/N�i�j

(5)In (5), the state i denotes that the total number of

infected node is i , and the state j denotes that the totalnumber new infected nodes is j . Because the state j iscompletely dependent on the current state i , we can modelthe entire process as a Markov process. Figure 2 shows thetransition probability graph for Markov process. Figure 2shows all possible transitions from state i to another state.Here, the state number inside the circle actually representsthe total number of infected node in the current state.

Consider that an infected node has an average of knumber of neighbors in a state i . Therefore, the maxi-mum number of newly infected nodes in the next state is



Figure 2. Transition probabilities from ith state to next statesfor Markov chain.

the minimum between the total susceptible nodes and thetotal number of susceptible neighbors of currently infectednodes. Formally,

max.j /Dmin.St ; ˛ � i � k/ (6)

Therefore, the expected number of new infected nodesin the next step is

EŒCtC1 D jCi jCt D i �D

max.j /XlD0

�Stl

�.p/l .1�p/St�l�l

(7)There is a critical parameter k that is the average num-

ber of neighbors of an infected node at each stage. In thisanalytical model, we assume that the nodes are uniformlydistributed in the whole network area. Therefore, node’sradio range plays an important role for identifying the num-ber of neighboring nodes. A good approximation is to findthe ratio of the covered region of the infected node to thetotal area of the entire region. This ratio can be used toestimate the number of neighbors of an infected node.

3.2.1. Area under the coverage.

Finding the area under the coverage of the multipleinfected nodes’ radio range is a challenging task, becausein a small area, compared with the number of infectednodes and their radio range, there are multiple overlappingof the covered area. Therefore, simple addition of the geo-metric covered area would not give the actual area coveredby multiple nodes. We assume that the wireless coverageof a node is represented by a circle where the radius of thecircle is equivalent to the radio range. We will use the term“circle as” the coverage area of nodes radio throughout thesection. To obtain the good approximation, we analyticallyestimate the area under the coverage in the following.

Consider there are n equal circles in a unit area wherethe radius of each circle is r . The area of i th circle is des-ignated as ai . We can find the actual area under coverage

Figure 3. Intersection of two circles.

with n circles �n using the inclusion-exclusion principle

�n D

ˇ̌̌ˇ̌ n[iD1

ai

ˇ̌̌ˇ̌

D

nXiD1

jai j �X

1�i<j�n

ˇ̌̌ai\aj

ˇ̌̌

CX

1�i<j<k�n

ˇ̌̌ai\aj\ak

ˇ̌̌

� � � � C .�1/n�1ˇ̌̌ai\: : :\an

ˇ̌̌

D nja1j �

n

2

! ˇ̌̌a1\a2

ˇ̌̌C

n

3

! ˇ̌̌a1\a2\a3

ˇ̌̌

� � � � C .�1/n�1ˇ̌̌ai\: : :\an

ˇ̌̌(8)

In (8), the unknown terms to find the actual coveragearea is the intersection area of multiple (2; 3; : : :; n) circles.The intersection areas are calculated in the following.

Case 1: When there is only one infected node, the areaunder the radio range of the node is the coveragearea of the infected node.

Case 2: When there are two infected nodes in an areaA,there is a possibility that the coverage area of thistwo nodes will overlap. Figure 3 illustrates one ofthe possible scenarios. In this figure, the circle aand the circle b are intersected with each other.The distance of their centers is `. We can find thecoverage area for both circle in the unit square Ausing the following theorem.

Theorem 1. The expected area of intersectionof two equal circles in a unit square is

R 2r0 2`.`2�

4 C̀�/��2r2 cos�1 .`=2r/�.`=2/

p4r2�`2

�d`

where r is the radius of each circle and ` is the



distance between the centers of the circles and0� `� 2r .

Proof . Consider that the radius of the circles ismuch smaller than each side of the unit square.Two circles intersect with each other if and onlyif 0 � ` � 2r . Therefore, the probability that twoarbitrary circles in a unit square intersect is equiv-alent to the probability of the distance between thecenters of the circles is less than 2r . The probabil-ity p.`/ of the distance between the centers of thecircles, `, is [28]

p.`/D 2`.`2 � 4`C �/ (9)

The intersection area of two circles is dependenton the radius of each circle, r , and the distancebetween the centers of the circle. The intersectionarea �2 is given by

�2 D 2r2 cos�1

�`

2r

��`

2

p4r2 � `2 (10)

In both (9) and (10), the only variable is `. Thevalue of ` can be varied from 0 to 2r . Therefore,the expected intersection area EŒ�2� between twoarbitrary circle in a unit square is

EŒ�2�D

Z 2r

0p.`/� �2 d`

D

Z 2r

02`.`2 � 4`C �/

�

�2r2 cos�1

�`

2r

��`

2

p4r2 � `2

�d`

(11)�

Case 3: Three circles can intersect in three ways.Because (11) utilizes only the intersection of threecircles, we are interested in the common intersec-tion area �3 of circles a, b, and c in Figure 4. Thefollowing theorem states the intersection area ofthree circles in a unit square.

Theorem 2. Consider three arbitrary cir-cles a, b, and c with radius r in a unitsquare. The probability of mutual intersec-tion of these three arbitrary circles in a unit

square is�2`.`2 � 4`C �/

��4r2 cos�1 .`=4r/

�.`=2/p16r2 � `2

�where

� ` is the distance between the centers of anytwo circles a and b and 0� `� 2r

� d is the maximum distance from the center ofthe circle c to the center of any circle a,band also 0� d � 2r

Proof . We prove this theorem in two parts.From Theorem 1, the probability of intersection

Figure 4. Intersection of three circles.

Figure 5. Possibility of third circle for intersection.

between two circles in a unit square is 2`.`2 �4`C�/ where the distance between the center ofthe circle is `. Because the probability states theintersection of two circle, for example, the circlea,b, we need to find out the probability of theintersection of the another circle, c, to both thecircles a,b. The condition of intersection of anycircle with circle c is that the distance between thecenters of the circle and circle c must be less than2r . In Figure 5, a0 and b0 denote the center of cir-cles a,b, respectively. We just draw two circleswith radius 2r concentric to a0 and b0, respec-tively. Both of the circles are shown by dashedline in Figure 5. Because the center c0 of the cir-cle c must be with the range of 2r from both a0and b0, c0 must lie inside the intersecting area ofthe two outer circles with radius 2r . The enclosedarea by the arc pqr and psr is the intersectionarea of the two outer circles.The area of the square A is equivalent to a unitsquare. Therefore, the area enclosed by the arcpqr and psr is equivalent to the probability of



having the center of an arbitrary circle. The dis-tance between the centers of the outer circle is `.Therefore, the enclosed area is

' D 4r2 cos�1�`

4r

��`

2

p16r2 � `2 (12)

The probability of mutual intersection of threecircles is

} D�2`.`2 � 4`C �/

��

�4r2 cos�1

�`

4r

�

�`

2

p16r2 � `2

�(13)�

Corollary 1. The expected mutual intersectingarea of three circles is

! D

Z 2r

0

Z 2r

0} � p.s/� �3 d` ds (14)

where p.s/ denotes the probability density fordistance s between the center c0 and any of thecenters a0 and b0 [29]

p.s/D

242sr2

0@2�

cos�1� s2r

��

s

�r

s1�

s2

4r2

1A35

(15)and �3 denotes the intersection area of threecircles [30].

Case 4: Calculation of intersecting area geometricallyfor more than three circles is (almost) unsolvablebecause exponential number of combinations inthe arrangement of four or more circles exhibitsthe complexity for finding a closed-form equa-tion to calculate the intersection area. Moreover,the intersecting area for two and three circlesdominate results than intersection of more circleswith small number of circles compared with largearea. Therefore, we restrain to find the closed-form equation of finding the expected area ofintersection for more than three circles.

In [31], Librino et al. devise an trellis-based itera-tive algorithmic solution to compute the intersec-tion area for more than three circles. The expectedmutual intersection area can be calculated usingthis algorithm with the intersection probability formore than three circles. We find combination inthe arrangement of different number of circles inan area experimentally and generate the probabil-ity of intersecting more than three circles in anarea from this combination.

In the aforementioned description, we have perceivedthe way of calculating the mutual intersection area for dif-ferent number of circles. This values can be inscribed in (8)to calculate the actual coverage area by different numberof overlapping circles in an area. Consider the total areacovered by the infected nodes Ct is A1. Then the value ofnumber of neighbors, k, is

k DA1

A�N

Ct(16)

3.2.2. Mobility parameter.

In (4), the meeting probability ˇ among the nodes is apivotal parameter. Because we consider a mobile network,the nodes’ movement pattern influences the meeting proba-bility. If the transmission range r is small compare with thearea size A, it has been shown that the exponential inter-contact time is a good approximation for both random waypoint and RDM model [32]. In [32], Jindal et al. presenteda meeting rate between any two nodes in an area whereall nodes follow the random direction model. Let NL be theepoch length, Nv the average node speed, NTstop the aver-age pause time after an epoch, and NT the expected epochduration. Let node x move according to the RDM from itsstationary distribution at time 0. Let y be a static node uni-formly chosen from the total nodesN . The expected hittingtime ETrd of node x and node y for the random directionmodel is given by

ETrd D

�A

2r NL

� NL

NvC NTstop

!(17)

If node y is also moving according to the RDM, then theprobability distribution of the meeting time EMrd for theRDM has an approximately exponential distribution andthe expected value

EMrd DETrd

pm OvrdC 2.1� pm/(18)

where Ovrd is the normalized relative speed for RDM andpm D NT =. NT C NTstop/ is the probability that a node is mov-ing at any time. The normalized relative speed for thisRDM model is Ovrd D 1:27 [32].

The expected time for any node x to reach any othernode in the network is

� DEMrd

N � 1(19)

Therefore, the rate of contact between any of two nodesin a network with N nodes that are moving according toRDM model is

�D1

�DN � 1

EMrd(20)



Because the intercontact times among the nodes areexponentially distributed, we can calculate the value ˇof (2) as

ˇ D 1� e�� (21)

3.2.3. Scheduling parameter.

The contact between an infected and susceptible is notalways guaranteeing a successful transmission of an object.There are three folds of contention that may occur for theevent of transmission in a wireless network. These are finitebandwidth, scheduling, and interference. In this paper, weonly consider the scheduling issue for the transmission.We have also utilized the transmission probability due toscheduling presented by Jindal et al. [32]. Let Esch repre-sent the event that a scheduling mechanism allows nodesx and y to exchange a object in a time unit. The schedul-ing mechanism prohibits any other transmission within onehop from the transmitter and receiver in the same time unit.The probability of this event P .Esch/ is dependent on theinterested transmitter–receiver pair that contending withthe x–y. Because we consider only the scheduling issuein the wireless network, it is obvious that

� D P .Esch/ (22)

Consider that there are a nodes within the one hop of thetransmitter and receiver pair and that there are c number ofnodes within two hopes but not in one hop of the x–y pair.EventEa denotes the existence of a nodes, andEc denotesthe existence of c nodes. Let t .a; c/ denote the expectednumber of possible transmission within the range of x–ypair. By symmetry, all contending pairs are equally likelyto capture the time slot and start transmission. Therefore,

P .EschjEa; Ec/D1

t.a; c/(23)

where t .a; c/ can be calculated using (23).

t .a; c/D

�1C papex

��a

2

�� 1

��Cacpcpex

2(24)

where

pa D1

16C

A

4�r2(25)

pc D3

20�

A

5�r2(26)

AD

Z 2r

r

x

2r2

r2 cos�1

x2 � 3r2

2rx

!

C 4r2 cos�1 x2C 3r2

4rx

!

�1

2

q.x2 � r2/.9r2 � x2/

�dx

(27)

The only unknown value of (23) is pex . The value ofpex can be calculated using (24)

pex D

N�1XmD1

2m.N �m/

N.N � 1/

N�1XiDm

1

N � 1

1

m.N �m/

�1Pi

jD11

j .N�j /

(28)

3.2.4. Getting the final result.

The values of ˛, ˇ, and � are derived analytically andcan be substituted in (2). Using these values, we can calcu-late the expected number of new infected nodes from (4).In the next section, we will present the rigorous simula-tion result and compare the result with analytically derivedvalues of infected nodes in each time unit.

3.3. Multiple objects diffusion

Consider a system where multiple objects will be dissem-inated in a network. Assume that there are m number ofobjects to be distributed in a network of N nodes whereN � m. Initially, each of the m objects will be held by asingle node. Therefore, the probability for a node to holdany object ism=N . Consider that a node n0 hasOt objectsat any instant t . The initial and terminal conditions of Otcan be described as

O0 Dm

N(29)

O1 Dm (30)

Each node has k average neighboring nodes. Withoutloss of generality, we can consider that each of the neigh-bors has also Ot number of objects at the time instantt . Consider that a node n0 and the neighboring nodes ofn0 have w different objects than the node n0. Considerthat Vk denotes the set of unique objects among k nodeswhere each of the k nodes contains O1

t ; : : :; Okt objects,

respectively. O0t denotes the set of objects in node n0.

Formally,

Vk �O1t [ : : :[O

kt

w � Vk nO0t

(31)

We will show the derivation for calculating the valueof w.

The k neighbors of node n0 hold total k �Ot elementson average at any time t . We consider two aspects for cal-culating the object difference between the node n0 and therest of the k neighbors. The aspects are as follows:

(1) All the objects that are held by k neighbors may notbe unique.

(2) There could be overlap of objects between the noden0 and the k neighbors.



To compute the first aspect, we must find the probabilityof unique objects among two nodes. The following theo-rem gives the probability of unique objects in k nodes ina network.

Theorem 3. The total expected number of unique objectsheld by k nodes in a network is

Vk D Vk�1C

OtXlD0

Ot

l

! m�Ot

Vk�1 �Ot C l

!

m

Vk�1

! � l (32)

where there total number of objects prevail in a networkis m and each node holds Ot number of objects at timeinstant t .

Proof . To proof the theorem, we need to establish the basecase when the number of node is 0 and 1.

Case kD0: When the number of node is 0, for example,k D 0, then

V0 D 0 (33)

Case kD1: If we consider only one node, then total num-ber of objects held by this node represents the totalnumber of unique objects. Here, each node con-tains Ot number of objects at any time instant t .Therefore,

V1 DOt (34)

Case k�2: Consider, two nodes na and nb in a networkwhere each of them holds Oat and Obt objects at anytime instant t among the total m objects in network.There are g objects that are in common between Oatand Obt . The nb node contain z number exclusiveobjects than the node na. Figure 6 shows the object

Figure 6. Set representation of object allocation between nodena and nb.

allocation between the nodes na and nb , the com-mon objects g, and the exclusive objects z in thenode nb . Formally,

g �Oat [Obt

z �Obt nOat

(35)

The probability of z exclusive objects in nb thanna is

p.z/D

Obtz

! m�Obt

Oat �Obt Cz

! m

Oat

! ; where Oat �Obt

(36)

The expected number of exclusive objects held bythe node nb is

EŒz�D

ObtXlD0

Obtl

! m�Obt

Oat �Obt C l

! m

Oat

! � l (37)

Therefore, the total number of unique objects heldby these two nodes is

V2 DOat C Total number of exclusive objects held

by node b

DOat CEŒz�

DOat C

ObtXlD0

Obtl

! m�Obt

Oat �Obt C l

! m

Oat

! � l

(38)

Consider that both nodes na and nb contain the aver-age number of objects, Ot . Therefore, Oat D O

bt D

Ot . Because Oat D Ot , the Oat can be replaced byV1. (38) can be expressed with respect to (34) as

V2 D V1C

ObtXlD0

Obtl

! m�Obt

V1 �Obt C l

! m

V1

! � l

D V1C

OtXlD0

Ot

l

! m�Ot

V1 �Ot C l

! m

V1

!

� lh* Obt DOt

i

(39)



Thus, we can write a general equation for totalunique objects held by k nodes in a network in arecursive fashion of (39),

Vk D Vk�1C

OtXlD0

Ot

l

! m�Ot

Vk�1 �Ot C l

!

m

Vk�1

! � l

(40)

�

Next, we calculate the second aspect where node n0 hassome objects that are also held by the k neighbors. BecauseVk denotes the total number of unique objects held by the kneighboring nodes of n0 andOt represents the total objectsin n0, we should find the number of common objects inbetween Ot and Vk . It is inevitable that Vk � Ot wherek � 1. The probability that there are g number of commonobjects in Vk and Ot is

p.g/D

Ot

g

! m�Ot

Vk � g

! m

Vk

! (41)

The expected number of common objects held by thetwo nodes is

EŒg�D

OtXlD0

Ot

l

! m�Ot

Vk � l

! m

Vk

! � l (42)

Thus, the total number of objects in Vk that are not inthe node n0 is

w D Vk �EŒg� (43)

In the system model, consider that every node possesenough bandwidth to send all the objects it holds andreceive all the objects it obtains from its neighbors in asingle transmission. Thus, in an ideal condition, the noden0 will receive all the w objects in the next round (tC 1).However, in wireless mobile network, the mobility andtransmission error play crucial role for data dissemination.The meeting probability ˇ between nodes in a mobile net-work is given in (21). Equation (22) provides the successfultransmission probability � of objects in wireless networkwhere multiple nodes can transmit simultaneously. Thus,

the expected number of objects that the node n0 will get inthe t C 1 round is

OexptC1 D w � ˇ � �

D .Vk �EŒg�/� ˇ � �

D

0BBBB@Vk �

OtXlD0

Ot

l

! m�Ot

Vk � l

! m

Vk

! � l

1CCCCA� ˇ � �

(44)

In (44), the variable Vk is dependent on the value of Ot .The Ot is a time-varying variable that denotes the aver-age number of objects in a node in the network at time t .The m is constant for particular network. The values ofˇ and � are dependent on the network parameter that hasbeen shown in the previous section. Therefore, (44) givesthe near perfect approximation of acquiring objects by anode in a network of epidemic dissemination for multipleobjects.

4. SIMULATION RESULTS

To verify the analytical model of epidemic diffusion ofdata, we developed a discrete event simulator in CCC.In simulation, we mimic the real-time scenario for mobilenetwork. We consider that peers use a distributed maximalindependent set algorithm [33,34] to find non-interferingnodes in a network. Members of an independent setcan transmit simultaneously without network interference.Note that maximal independent set of a wireless mobilenetwork changes because of mobility of nodes. Considerthat L is the number of maximum independent sets duringthe cycle t and Si .t/ is the i th independent set. Then thefollowing equality holds:

N DX

1�i�L

jSi .t/j (45)

The distribution cycle is divided into the L number ofslots; that is, the total number of slots in a cycle is equiv-alent to the number of maximum independent sets. A peerp 2 Si .t/ transmits only during the i th slot.

In simulation, we focus on a wireless network with dif-ferent node densities on a square area of 500 m2. The totalnumber of nodes varies in the areas from 100 to 200 nodes.Initially, these nodes are randomly distributed throughoutthe simulation area. We assume that nodes mobility patternfollows RDM model with a mean speed of 1–5 m/s andmean pause time before changing direction of movementis 0 s. We consider this setting that will represent the cus-tomers mobility within a mall to a slow moving vehicle ina city. We assume nodes to be equipped with a standardIEEE 802:11 interface. We experiment with different radiotransmission ranges from 20 to 60 m.

We simulate both single object and multiple objects sce-narios separately and compare the simulation results with



our analytical results. For single object diffusion, a node ischosen randomly and given an object. This object is dif-fused in the entire network. In multiple object diffusion,each node holds a unique object. The simulation terminateswhen all nodes get all the objects presented in the network.

4.1. Single object diffusion

This section discusses the validity of the presented analyt-ical model for single object data diffusion through simula-tion. For the simulation, an object is given to a randomlychosen node in the network. This node broadcasts thisobject to its neighbors. This process continues until all thenodes in the network obtain that object.

Figure 7 shows the comparison of the analytical resultswith the simulation results. In this figure, the number ofinfected nodes is plotted with the passage of time. Theresult shows that both the analytical results and the simula-tion result match with close proximity. The analytical resultindicates little slower infection rate than the simulationresult in the beginning. Later, the analytical result coin-cides with the simulation result. This behavior is expectedbecause all the neighbors of the infected node in simula-tion effected immediately and so on. On the contrary, everystep in the analytical result, the number of neighbors iscalculated on the average of the entire area.

In the epidemic data dissemination, the number of nodesand their speed of moving are key factors. We consider dif-ferent number of nodes moving in a 500 m � 500 m areawhere each node has a radio range of 30 m. In Figure 8,we can observe that the time for object diffusion amongall the nodes decreases with the increase of nodes. How-ever, the enormous increase of nodes in terms of data dis-tribution area may not follow the same result. This factcan also be observed from the same figure. The rate ofdecrease for data diffusion time declines with the increaseof the number nodes. The similar argument also holds forthe speed of the nodes. The data diffusion rate increases

(alternatively, data dissemination time decreases) withchanging the node speed of the mobile modes from 1 to2 m/s. Nevertheless, data diffusion rate increases when thenodes move with 3 m/s. However, the rate of increase issufficiently lower than the previous step. Our proposedanalytical model is able to anticipate all the aforemen-tioned scenarios as expected. In our analytical model, weconsider the number of nodes, the scheduling among thenodes for data broadcasting, and the speed of the nodes.Figure 8 shows that our analytical result gives the almostaccurate result.

Figure 9 shows the impact of radio range and the speedof nodes for object dissemination. With larger radio range,a node can communicate with more number of nodes at atime. Thus, a node can transmit and receive object to andfrom many nodes than the nodes with smaller radio range.However, the larger radio range does not only bring ben-efit. Instead, it has some drawbacks in scheduling-basedbroadcasting. In scheduling-based broadcasting, whereasa node gets the opportunity to broadcast its objects, noneof its neighbors is able transmit object. With larger radiorange, a node has many neighbors. Thus, a node has towait long time to get its turn to broadcast. In addition,larger radio range increases the chance of collision of trans-mitted objects. Therefore, the data dissemination does notincrease linearly with the increase of radio range. In theprevious paragraph, we have already discussed the impactof mobility on data dissemination. Figure 9 also showsthe analytical and simulation results of data dissemina-tion among 100 nodes with different radio ranges and thenode speeds. The difference of data diffusion time betweenthe analytical and the simulation ones is less than 10% inall cases. Therefore, the result reveals that our proposedanalytical model provides an optimistic prediction aboutdata diffusion pattern and delay for entire network. Themain reason of near perfect prediction is that this modelalso considers the average number of neighbors of infectednodes at each step of progression.

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140 160 180

Infe

cted

Nod

es

Time

Area: 500mX500m, Total Node : 200

Simulation

Analytical

Figure 7. Comparison of analytical and simulation model for radio range 20 m.



100

150

200

250

300

350

400

450

500

550

600

650

50 75 100 125 150

Obj

ect

Acq

uisi

tion

Tim

e

Number of Nodes

Radio Range : 30 m

1 m/s (Simulation)

1 m/s (Analytical)

2 m/s (Simulation)

2 m/s (Analytical)

3 m/s (Simulation)

3 m/s (Analytical)

Figure 8. Comparison of analytical and simulation model for different number of nodes.

0

50

100

150

200

250

300

20 25 30

Obj

ect

Acq

uisi

on T

ime

Radio Range

Total Node : 100 2 m/s (Simulation)

2 m/s (Analytical)

3 m/s (Simulation)

3 m/s (Analytical)

Figure 9. Comparison of analytical model and simulation result with the impact of mobility.

100

110

120

130

140

150

160

170

180

190

200

0 5 10 15 20 25 30 35 40 45 50

Acq

uire

d ob

ject

s

Rounds

Total Nodes : 200, Speed : 2 m/s, Radio Range : 35 m

Analysis

Simulation

Figure 10. Comparison of analytical model and simulation of data dissemination.

4.2. Multiple object diffusion

In the multiple object diffusion simulation, a nodeexchanges all the objects it has in the meeting with other

nodes. The simulation terminates when all the nodes in thenetwork acquired all the objects prevail in the network.

Figure 10 shows the analytical results and simulationresults for object dissemination pattern in the network for



0

10

20

30

40

50

60

70

80

90

1 2 3 4 5

Num

ber

of R

ound

s

Speed (m/s)

Node : 200, Object : 200, Radio Range : 50m

Analysis

Simulation

Figure 11. Comparison of analytical model and simulation with the impact of mobility.

0

15

30

45

60

75

90

105

120

135

35 40 45 50 55 60

Num

ber

of R

ound

s

Radio Range

Node : 200, Object : 200, Speed : 2 m/s

Analytical

Simulation

Figure 12. Comparison of analytical model and simulation with the impact of radio range.

200 nodes. The speed of each node is 2 m/s, and the radiorange of each node is 35 m. A node will get 200 objectsat the data diffusion process. The figure displays the resultfor required rounds for a node to acquire last 100 objectsamong 200 objects. The initial round for achieving first 100objects for a node in the simulation is considered as the sta-bility phase. Figure 10 depicts that the progression of datadissemination among the nodes according to the analyticalresult almost coincides with simulation result.

Different from other related works in the literature, ouranalytical model considers the mobility and speed of thenodes for data dissemination. Figure 11 shows the impactof nodes’ speed in data dissemination. In simulation, thenodes’ speed is varied from 1 to 5 m/s. With the increas-ing speed, the dissemination of data among the nodes isfaster. Because the radio range is 50 m in this experiment,the increased speed up to 5 m/s also increases the numberof new neighbors per round. Therefore, the exchange ofobjects between the nodes increases. The analytical resultalso reveals the similar results as shown in the Figure 11.

The counter impact of radio ranges for multiple objectdissemination is shown in Figure 12. With the larger radiorange, the number of neighbors of node increases. There-fore, a node distribute objects to more nodes in a singlebroadcast. Besides, a node also receives more object fromits neighbor with larger radio range. However, the largerradio range has also negative impact on data dissemination.Nevertheless, the large radio range increases the collisionof data in simultaneous broadcast. Moreover, the schedul-ing probability � for a node also decreases with larger radiorange. The simulation result clearly reveals this scenario inFigure 12. The total number of rounds to acquired all theobjects does not decline in a straight line with the increaseof radio range. The analytical results also follows sametrend with the simulation results.

We have simulated the impact of data dissemination onnode densities. The number of nodes is varied from 100 to200. At the beginning of the simulation, each node carriesa unique object. For, example, when the number of nodesis 150, the total number of objects in the system is also



0

10

20

30

40

50

60

70

80

100 125 150 175 200

Num

ber

of R

ound

s

Number of Nodes

Area : 500mX500m, Speed : 2 m/s, Radio Range : 50m

Analysis

Simulation

Figure 13. Comparison of analytical model and simulation with different node densities.

150. Figure 13 shows the data dissemination pattern withthe varying number of nodes. It considers the total roundrequired for acquiring 80% of total objects. When the nodedensity increases, the data exchange rate among the nodesalso increases. As a result, the total number of rounds foracquiring objects is also decreased. However, the rate ofdecrease from 100 nodes to 125 is not equivalent to thedecrease of total rounds from 175 to 200 nodes becausetoo many nodes in a small area also increases the collisionof data broadcast. In Figure 13, the analytical result alsofollows the same pattern for decreased number of roundswith the increased of node densities. However, there is adifference between the analytical and simulation results.We have utilized data from simulation for calculating theaverage number of neighbors for a node. This average num-ber of neighbors is fixed in the analytical results. However,in simulation, the average number of nodes is different ateach step of the simulation. Moreover, the meeting andscheduling probabilities among the nodes in the analyticalresults are determined according to the number of nodes,their radio range, mobility pattern, and the speed of thenode. This probability values remain the same in thestepwise calculation in analysis. The differences betweenthe analytical and simulation results in initial stage arepropagated to the later stages.

5. CONCLUSION

We have presented analytical models for contagion datadissemination in wireless mobile network. We have consid-ered both the single and multiple object diffusion processesin mobile network and propose the appropriate analyti-cal model for each of them. Our analytical models can beused to estimate the expected time/delay of object diffu-sion among the mobile nodes. The models and observa-tions reveal the suitability of the epidemic process usingspatial demand-based algorithm for information diffusion.Because the number of nodes in the system is fixed andthe next state of the system is completely dependent onthe current state, we have modeled the epidemic baseddata diffusion system as a Markov process and analyzed

the behavior of the system. The analysis reveals the com-plex inter-relationship of node speed, wireless radio range,scheduling among the nodes for data broadcast, and nodedensities on object diffusion rate. In addition, for multi-ple object data diffusion, we have developed a progres-sive analytical model for objects exchanging pattern for anode. Simulation results show that our analytical modelis accurately apprehended the dynamics (the number ofnodes, their radio ranges, and the speed of the nodes)of data dissemination in wireless mobile network. Theresults imply that the object propagation rate experiencesa phase transition as a function of node densities, radiorange, and node speed in a mobile network, both single andmultiple objects.

ACKNOWLEDGEMENTS

This research has been financially supported by the Natu-ral Sciences and Engineering Research Council (NSERC)of Canada and Ontario Graduate Scholarship (OGS).

REFERENCES

1. Feng J, Xu L, Ramamurthy B. Overlay constructionin mobile peer-to-peer networks. Mobile Peer-to-PeerComputing for Next Generation Distributed Environ-ments 2009; 1: 51–67.

2. Cao H, Wolfson O, Xu B, Yin H. MOBI-DIC: mobilediscovery of local resources in peer-to-peer wirelessnetwork. IEEE Database Engineering Bulletin 2005;28(3): 11–18.

3. Goel SK, Singh M, Xu D, Li B. Efficient peer-to-peerdata dissemination in mobile ad-hoc networks, In Pro-ceedings of the 31st International Conference on Par-allel Processing Workshops, Vancouver, BC, Canada,August 2002; 152–158.

4. Luo Y, Wolfson O, Xu B. A spatio-temporal approachto selective data dissemination in mobile peer-to-peer



networks, In Proceedings of the 3rd InternationalConference on Wireless and Mobile Communica-tions, Guadeloupe, French Caribbean, March 2007;50b–50b.

5. Li M, Lee W-C, Sivasubramaniam A, Zhao J. SSW:a small-world-based overlay for peer-to-peer search.IEEE Transactions on Parallel and Distributed Sys-tems 2008; 19(6): 735–749.

6. Ku W-S, Zimmermann R. Nearest neighbor querieswith peer-to-peer data sharing in mobile environ-ments. Pervasive and Mobile Computing 2008; 4(5):775–788.

7. Loulloudes N, Pallis G, Dikaiakos MD. Informationdissemination in mobile CDNs. Content Delivery Net-works 2008; 9: 343–366.

8. Xing B, Deshpande M, Venkatasubramanian N,Mehrotra S, Bren D. Towards reliable applicationdata broadcast in wireless ad hoc networks, InProceedings of the IEEE Wireless Communicationsand Networking Conference, Hong Kong, March 2007;4063–4068.

9. Park K, Choo H. Energy-efficient data disseminationschemes for nearest neighbor query processing. IEEETransactions on Computer 2007; 56(6): 754–768.

10. Jacquez JA. A note on chain-binomial models of epi-demic spread: what is wrong with the reed-frost formu-lation? Mathematical Biosciences 1987; 87(1): 73–82.

11. Dietz K. Epidemics: the fitting of the first dynamicmodels to data. Journal of Contemporary Mathemat-ical Analysis 2009; 44(2): 97–104.

12. Andersson H, Britton T. Stochastic Epidemic Modelsand their Statistical Analysis, (1st edn). Springer:New York, USA, 2000.

13. Papadopouli M, Schulzrinne H. Design and imple-mentation of a peer-to-peer data dissemination andprefetching tool for mobile users, In Proceedings of the1st NY Metro Area Networking Workshop, New York,USA, March 2001; 1–7.

14. Olafur RH, Karlsson G. On the effect of cooperationin wireless content distribution, In Fifth Annual Con-ference on Wireless on Demand Network Systems andServices, Garmisch-Partenkirchen, Germany, January2008; 141–148.

15. Zhang X, Neglia G, Kurose J, Towsley D. Performancemodeling of epidemic routing. Computer Networking2007; 51(10): 2867–2891.

16. Haas ZJ, Small T. A new networking model forbiological applications of ad hoc sensor networks.IEEE/ACM Transactions on Networking 2006; 14(1):27–40.

17. Khelil A, Becker C, Tian J, Rothermel K. An epi-demic model for information diffusion in MANETs. InProceedings of the 5th ACM International Workshop

on Modeling Analysis and Simulation of Wireless andMobile Systems. ACM: New York, NY , USA, 2002;54–60.

18. Mundinger J, Weber RR, Weiss G. Analysis of peer-to-peer file dissemination amongst users of differentupload capacities. SIGMETRICS PerformanceEvaluation Review 2006; 34(2): 12–14.

19. Özkasap Ö, Çaglar M, Cem E, Ahi E, Iskender E. Step-wise fair-share buffering for gossip-based peer-to-peerdata dissemination. Computer Networks 2009; 53(13):2259–2274.

20. Özkasap Ö, Çaglar M, Yazici ES, Küçükçifçi S.An analytical framework for self-organizing peer-to-peer anti-entropy algorithms. Performance Evaluation2010; 67(3): 141–159.

21. Bakhshi R, Gavidia D, Fokkink W, van Steen M.An analytical model of information dissemination fora gossip-based protocol. Computer Networks. Spe-cial Issue on Gossiping in Distributed Systems 2009;53(13): 2288–2303.

22. IEEE 802.11. IEEE 802.11 web-site, 2009. Availablefrom: http://www.ieee802.org/11/ [accessed on 1 May2011].

23. Lao L, Cui J-H. Reducing multicast traffic loadfor cellular networks using ad hoc networks. IEEETransactions on Vehicular Technology 2006; 55(3):882–830.

24. Luo H, Ramjee R, Sinha P, Li L, Lu S. UCAN: a uni-fied cellular and ad-hoc network architecture, In Pro-ceedings of the 9th Annual International Conferenceon Mobile Computing and Networking (MobiCom),California, USA, September 2003; 353–367.

25. Lin Y-D, Hsu Y-C. Multihop cellular: a new archi-tecture for wireless communications, In Proceedingsof the IEEE INFOCOM, Tel Aviv, Israel, April 2000;1273–1282.

26. Carofiglio G, Chiasserini C-F, Garetto M, Leonardi E.Route stability in manets under the random direc-tion mobility model. IEEE Transactions on MobileComputing 2009; 8(2): 1167–1179.

27. Islam MT, Akon M, Shen XS. SPID: a novel P2P-based information diffusion scheme for mobile net-works, In Proceedings of the IEEE GLOBECOM,Hawaii, USA, November 2009; 4185–4190.

28. Weisstein EW. Square line picking, 2011.Available from: http://mathworld.wolfram.com/SquareLinePicking.html [accessed on 1 May 2011].

29. Solomon H. Geometric Probability, (1st edn). SIAM:Pennsylvania, 1978.

30. Fewell M. Area of common overlap of three cir-cles. Technical Report, Defence Science and Tech-nology Organisation, Edinburgh South Australia 5111Australia, 2006.



31. Librino F, Levorato M, Zorzi M. An algorithmic solu-tion for computing circle intersection areas and itsapplications to wireless communications, In Proceed-ings of the 7th International Conference on Modelingand Optimization in Mobile, Ad Hoc, and WirelessNetworks, Seoul, Korea, June 23; 239–248.

32. Jindal A, Psounis K. Contention-aware performanceanalysis of mobility-assisted routing. IEEE Transac-tions on Mobile Computing 2009; 8: 145–161.

33. Moscibroda T, Wattenhofer R. Maximal independentsets in radio networks, In Proceedings of the 24thAnnual ACM SIGACT-SIGOPS Symposium on Princi-ples of Distributed Computing, Las Vegas, USA, June2005; 148–157.

34. Shi Z. Self-stabilization protocols, and distributedprotocols in mobile ad hoc networks, PhD Disserta-tion, Clemson University, SC, USA, 2005. Adviser-Goddard, Wayne.

AUTHORS’ BIOGRAPHIES

Mohammad Towhidul Islam re-ceived his B.Sc.Engg., M.Comp.Sc.,and Ph.D. degree from the BangladeshUniversity of Engineering andTechnology (BUET), Bangladesh;University of Manitoba, Canada;and University of Waterloo, Canada,respectively. His current research

interests include mobile peer-to-peer computing andapplications, service-oriented architectures, and mobilecomputing. In recent days, he is mostly devoted to developanalytical model for context-based data disseminationbesides his software industry commitment.

Mursalin Akon received his B.Sc.Engg., M.Comp.Sc., and Ph.D. degreefrom the Bangladesh University ofEngineering and Technology (BUET),Bangladesh; Concordia University,Canada; and University of Waterloo,Canada, respectively. His currentresearch interests include peer-to-peer

computing and applications, network computing, andparallel and distributed computing.

Atef Abdrabou received his Ph.D.degree in 2008 from the Universityof Waterloo, Ontario, Canada, inelectrical engineering. In 2010, hejoined the Department of ElectricalEngineering, UAE University, Al-Ain, Abu Dhabi, UAE, where heis an assistant professor. He is a

corecipient of a Best Paper Award of IEEE WCNC2010. He also received the prestigious National Scienceand Engineering Research Council of Canada (NSERC)postdoctoral fellowship for academic excellence andresearch potential in 2009. His current research inter-ests include network resource management, QoS provi-sioning, and information dissemination in self-organizingwireless networks.

Xuemin (Sherman) Shen receivedhis B.S. (1982) degree from theDalian Maritime University, China,and M.Sc. (1987) and Ph.D. degrees(1990) from Rutgers University,New Jersey, all in electrical engi-neering. He is a professor and uni-versity research chair, Department

of Electrical and Computer Engineering, University ofWaterloo. His research focuses on mobility and resourcemanagement, UWB wireless networks, wireless networksecurity, and vehicular ad hoc and sensor networks. Heserved as an area editor for IEEE Transactions on Wire-less Communications and editor-in-chief for Peer-to-PeerNetworks and Applications. He is a distinguished lecturerof the IEEE Communications Society, Fellow of IEEE, andFellow of Engineering Institute of Canada.


Modeling epidemic data diffusion for wireless...

Documents

Transcript of Modeling epidemic data diffusion for wireless...