An Obstacle Based Realistic Ad-Hoc Mobility Model for Social Networks

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1 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE An Obstacle Based Realstc Ad-Hoc Moblty Model for Socal Networks P. Venkateswaran Dept. of Electroncs & Tele-Communcaton Engneerng Jadavpur Unversty, Kolkata , INDIA Rahul Ghosh, Artra Das, S.K. Sanyal, and R. Nand Dept. of Electroncs & Tele-Communcaton Engneerng Jadavpur Unversty, Kolkata , INDIA Abstract An effcent deployment of a moble ad-hoc network (MANET) requres a realstc approach towards the moblty of the hosts who want to communcate wth each other over a wreless channel. Snce ad-hoc networks are drven by human requrements, nstead of consderng the random movement of moble nodes, we concentrate on the socal desre of the nodes for gettng connected wth one another and provde here a framework for the moblty model of the nodes based on Socal Network Theory. In ths paper, we capture the preferences n choosng destnatons of pedestran moblty pattern on the bass of Socal Factor ( F ) and try to fnd out the essental mpact of F on the Pause Tme of the nodes. Also, nstead of consderng an unobstructed terran, we carry out our smulatons n presence of obstacles whch block the node movement. Thus, we present here a more realstc moblty dstrbuton pattern. Further, a relatve comparson of the proposed model wth the popular Random Way-Pont (RWP) Model s also done. Index Terms MANET, moblty, Socal Network Theory I. INTRODUCTION In an ad-hoc network, a group of moble users, strewn across a locaton, desre to nteract wth each other over a wreless channel wthout any centralzed control. Such networks are helpful n emergency search and rescue operaton, n battlefelds, and for settng up nstant communcaton among the busness delegates assemblng n a lecture hall. In some cases, the topology of the network remans stable after an ntal setup perod, for example, once the busness delegates are seated around a table or n ther respectve rooms, ther laptops may be moved farly nfrequently. In some other cases, the network topology may be subjected to a rapd change due to frequent lnk falure and the moblty of the nodes. Based on the paper An Effcent Socal Network-Moblty Model for MANETs, prelmnary verson publshed by Rahul Ghosh, Artra Das, P. Venkateswaran, S. K. Sanyal and R. Nand whch appeared n the Proceedngs of the Internatonal Workshop on Dstrbuted Computng IWDC 2005, IIT Kharagpur, Inda, December Sprnger-Verlag Berln Hedelberg Further, wreless channels experence hgh fluctuaton n channel qualty due to several reasons ncludng multpath, fadng, dynamc change n topology and obstacles. For ths reason, nstantaneous creaton of such networks and ts mantenance s not an easy task. For provdng an envronment for specfc advantages over real world studes of MANET, smulaton s performed; an mportant component of whch s the moblty model. Once the nodes are ntally placed wthn an ad-hoc envronment, the moblty dstrbuton of the nodes dctates the effcency of the network. Wth the help of these dstrbutons, quanttatve nformaton can be drawn on the lnk change rate, successful packet delvery and the degree of connectvty of moble hosts. A good number of research works have been publshed regardng dfferent ssues lke routng protocols, moblty model, Qualty of Servce (QoS), bandwdth optmzaton for MANETs. In the absence of establshed propertes of real moblty patterns, t s not yet clear today, what are the essental parameters to consder whle constructng a moblty model [1]. The current scenaros on the avalable moblty models for MANETs are synthetc models based on smple, homogeneous, random processes [2, 3]. For example, Random Walk Moblty Model s used to represent pure random movements of the enttes of a system. A slght enhancement of ths s the Random Way-Pont (RWP) Model, n whch wayponts are unformly dstrbuted over the gven convex area and the nodes have so called thnkng tmes (pause tmes) before movng to next destnaton. Alternately, the wayponts can be unformly dstrbuted on the border of the doman, and ths model s referred to as the "Random Way-Pont on the Border" (RWPB) model. The spatal node densty resultng from RWPB model s qute dfferent from the RWP model,.e. the probablty mass shfts from the center of the area to the borders [4]. However, all such synthetc movement models generally do not reflect the real world stuatons regardng the moblty of nodes. In practce, a moble user, wthn a campus or n any geographc locaton does

2 38 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE 2006 not roam about n a random manner. Though the present synthetc models are more tractable for mathematcal analyss and easy for trace generaton, they do not capture the delcate detals lke tme-locaton dependence and communty behavor of pedestran moblty. Human decsons and socalzaton behavor play a key role n typcal ad-hoc networkng deployment scenaros of dsaster relef teams, platoon of solders etc. In [5,6], the authors used SNMP and syslog trace obtaned from access ponts to get partal nformaton about moblty, but these traces are based on usage pattern and may fal to represent the socal dmensons. In ths paper, we emphasze on the moblty pattern of ndvdual nodes based by strength of socal relatonshps. The revews of the socal network analyss may be found n [7]. We argue n favor of the socal behavor of the moble nodes and try to fnd out effects of these behavors on ther movement. Here, we have systematcally developed some socal ndcators out of the needs of an ad-hoc envronment and then, we have transformed t nto mathematcal doman to formulate key factors. These factors are then mapped to a topographcal space to show the dstrbuton pattern for our model. Thus, we present the desgn and analyss of the ndvdual as well as group moblty model based on the socal network theory. The proposed moblty model s made more realstc wth the ncorporaton of obstacles n the smulaton scenaro. The obstacles placed wthn the network area may represent, for example, the buldngs, trees etc n a college campus and these obstacles block the node movement as well as sgnal transmsson. The smulaton results show sgnfcant effect on node dstrbuton due to the presence of these obstacles, whch n turn would have a great mpact on the ad-hoc network performance. The rest of the paper s organzed as follows: In secton II, we gve a bref overvew of the related works. Secton III provdes an ntroducton to the concept of socal network theory. In secton IV, the proposed moblty model s presented. Secton V provdes our smulaton results and analyss. Fnally, the concluson s gven n secton VI. II. RELATED WORKS A great deal of attenton has been pad towards fndng out a realstc moblty model for MANET and the performance of the ad-hoc protocols under these moblty models. Such examples nclude [3, 8, 9]. Whle [8] gves a moblty model based on groupng of the moble nodes, [9] descrbes scale-free and stable structures n complex ad-hoc networks. The authors of [10] have ntroduced a canoncal moblty measure to predct lnk change rates for varous smulaton scenaros. However, the basc models adopted by them for smulaton envronment are the RWP model, the Random Gauss-Markov (RGM) model [11], and the Reference Pont Group Moblty (RPGM) model [12]. In [13], moblty pattern s obtaned from the survey-based approach and from the smulaton results of ther model, the authors suggest that convergng to a steady state dstrbuton s not necessarly a requrement of realstc moblty models. Mathematcal models of complex and socal networks have been shown to be useful n descrbng many relatonshps, ncludng real socal relatonshps [14]. In [15], an approach has been presented towards a moblty model on the relatonshps of people though the paper lacks a rgorous mathematcal representaton of the relatonshp between ndvduals. The authors of [16] have presented a moblty model based on Socal Network Theory from a theoretcal pont of vew. The socal network s represented usng a weghted graph, where weghts assocated wth each edge of the network are ndcators of drect nteractons between ndvduals. Fgure 1. The relatonshps between dfferent socal neghbors have been shown as the weght of the connectng edges. Deeper edges ndcate deeper connectvty. Interestngly, the degree of socal connectvty s ndependent of geographcal locatons. They have used a matrx, called Interacton Matrx, whose dagonal elements are 1 and other elements m j (lyng between 0 and 1) represent the nteracton between two ndvduals and j. Ther work provdes a framework for the mathematcal analyss based on the socal relatonshps of the nodes; but certan assumptons make ther formulatons unsutable for mplementaton n real world cases. Incluson of obstacles n the network smulaton has been performed n [3], wheren the obstacles are used both to defne movement pathways for moble nodes and to obstruct the transmsson between the nodes. The nodes move n the network area usng pre-defned paths whch are determned from the Vorono dagram of the obstacle vertces. Nodes are randomly dstrbuted along the paths and selecton of the path to reach destnatons s determned by shortest-path route computatons. The obstructon cone n whch the obstacles block wreless transmsson s also calculated n [3]. Though the paper uses the obstacles effectvely to desgn a moblty dstrbuton pattern, the assumpton of randomness makes ths model unrealstc and unsutable for properly modelng real world stuatons.

3 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE III. SOCIAL NETWORK IN AD-HOC MODE A network s a set of tems, whch are called vertces or sometmes nodes, wth connectons between them, called edges. There has been extensve study of networks n the form of mathematcal graph theory. Networks have also been studed extensvely n socal scences. These nvolve calculatng the nteracton between ndvduals and reconstructng the network such that vertces represent the ndvduals and the edges represent the nteracton between them. Typcal socal network studes address ssues of centralty and connectvty. Before gong nto the detaled dscusson of socal network theory, we would lke to explan the followng terms for clarty. Vertex: Ths fundamental unt of a network s also called a node n case of computer networks. Users are denoted by vertces. Edge: It s the lnk between the nodes. For socal networks, they can carry weghts representng, say, how well people know each other. They may also be drected, pontng only n one drecton. Drected / Undrected: An edge s drected f t runs only n one drecton and undrected f t runs n both drectons. Graphs contanng drected edges are called drected graphs or dgraphs. Degree: It s the number of edges connected to a vertex. For socal networks, t can be used as one of the measures of degree of nteractons. Component: The component to whch a vertex belongs s that set of vertces that can be reached from t by paths runnng along the edges of the graph. From the pont of vew of a socal network n an ad-hoc mode, these are the nodes wth whom the node under consderaton can make nteractons. A socal network can be defned as a set of people wth some defnte pattern of contacts or nteractons between them. The patterns of frendshp between ndvduals, busness relatonshp between companes and ntermarrage between famles are all examples of such networks. Tradtonal socal network studes often suffer from problems of naccuracy, subjectvty and small sample sze. Survey data, whch s the basc source of data for socal network studes, are nfluenced by subjectve bases on the part of the respondents;.e.; how one defnes degree of frendshp could be qute dfferent from how another one does. Although much effort s devoted for elmnatng possble sources of nconsstency, there remans large and uncontrolled errors n these studes. Because of these flaws, many other methods have been adopted for probng socal networks. One source of relatvely relable data s from collaboraton networks, whch are afflaton networks n whch partcpants collaborate n groups and lnks between them are establshed by common group membershp. Another relable source of data about personal connectons s from communcaton records of certan knds lke mals, telephone calls etc. The Moble Ad-Hoc Networks are a type of technologcal networks, a wreless network establshed between computers or other devces for the exchange of nformaton. But the moble devces are usually carred by humans and hence movement of such devces s based on human decsons and socalzaton behavor. In order to capture ths socal dmenson, t s mportant to model the behavor of ndvduals movng n groups at dfferent locatons under dfferent constrants. Heren comes the applcaton of socal network theory n ad-hoc mode of networks. The results of socal network theory can be used to effectvely model human behavor and whch can be used to desgn a near-actual moblty dstrbuton of nodes n an ad-hoc envronment on the bass of whch the ad-hoc protocols can be formulated. IV. THE PROPOSED MODEL Instead of usng heurstc approach, we develop our moblty model on the bass of the followng assumptons, whch also make our model more advantageous than the popular RWP model. The assumptons are: A 1 : The moble nodes tend to select a specfc destnaton and follow a well-defned path to reach that destnaton. A 2 : Path selecton process s based by the socal nteracton and communty demand and t s dfferent at dfferent locatons and tme. A 3 : The pause tme of the nodes beng a functon of socal network, s not random. Instead, t follows a specfc user orented dstrbuton at dfferent locatons. Wth the help of these assumptons, we try to fnd out the factors controllng the moblty of nodes and then study the effect of the factors on both the ndvduals and the groups. In all subsequent part of the paper, the terms host, node and ndvduals are equvalent and ndcate a sngle movng entty n the MANETs. A. Dfferent socal ssues controllng moblty In order to capture the socal tes nto a mathematcal relaton, we use the recent results n socal network theory. We represent a socal network usng a weghted graph where weghts assocated wth each edge of network are an ndcator of the drect nteractons between ndvduals. We assgn a value n the range [0, 1] to sgnfy the degree of socal nteracton between two people, where 0 ndcates no nteracton and 1 ndcates strongest socal nteracton. Snce every relaton between two moble nodes s not strong, we ntroduce here the term Connecton Threshold (CT), whch ndcates a lmt of socal connectvty. Contrary to [16], we do not assgn an arbtrary value to CT and express t as a functon of tme, network

4 40 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE 2006 parameters and socal ssues. In ths context, we defne the followng terms: Lnk Duraton [LD (t)]: The average tme duraton along whch a channel s formed between two moble nodes. Frequency of Connectvty [FC]: The number of tmes a moble node s connected to j over a sngle exstng tme of ad-hoc network. Let us frst dscuss how CT depends on LD (t) and FC. A hgh value of lnk duraton between two nodes suggests that the socal nteracton between them s consderably hgh. Agan, frequent connectvty between two nodes through out the lfe-tme of the MANET s ndcatve of the fact that the nodes prefer specfc socal relaton nstead of general socal relaton nvolvng large number of nodes. On the bass of the above, we relate CT wth LD(t) and FC as follows: the connecton threshold of a node j denoted by CT j n a group of n number of nodes s defned as CT n LD ( t) * FC 1 j (1) n * Ttotal where, n = total no. of nodes present n the current MANET wth whom the node j gets connected and T total = total tme elapsed by the node j n an ad-hoc envronment. A close observaton to (1) reveals the fact that CT depends on both the total amount of socal lnks formed and the hgh socal relatonshp between two moble nodes. Snce the total tme elapsed by the node j n an ad-hoc envronment s much greater than the total communcaton tme between two nodes, we can argue that n CT 1 as LD ( t) * FC < T total. 1 Agan, a lower value of CT suggests greater socal nteracton. It s to be noted that low value of CT s acheved by a hgh value of n.e. the no. of separate socal nteractons a node performs reflect the real socal network crtera. In order to gve a quanttatve dea on the value of CT, we consder an ad-hoc envronment n whch T total for a node s 30 mnutes. The Tables I & II, elucdate the dependence of the value of connecton threshold for two nodes on ther socal behavors. Clearly, n case of node 1 the effect of more number of dfferent socal lnks and short duraton of connectvty wth the socal neghbors reflect n the low value of CT; whereas the node 2 possesses a hgh value (more than four tmes than node 1) of CT due to the greater nteracton wth a specfc number of hosts. Interactng Nodes TABLE I. CONNECTION THRESHOLD FOR NODE 1 LD (sec) FC CT TABLE II. CONNECTION THRESHOLD FOR NODE Interactng Interactng Nodes LD (sec) FC CT Nodes Now, we determne the relatonshp of a node wth each of ts neghbors ndvdually. For ths, we construct a row matrx for each node n the moble network, where each element desgnates the nter-relatonshp between the node and one of ts neghbors. We denote the generc element of our matrx by k j. Thus, for a node, k j represents the nteracton of the node wth node j. It s evdent that the value of k j les between 0 and 1. It s worthwhle to menton that, whle constructng the matrx, we consder only those neghbors who have a reasonable socal nteracton wth the node,.e. all the k j n the matrx must le above the threshold value of CT for the node. Tll now, we have consdered only a sngle network topology. A property that s common to many networks s the communty structure, the dvson of network nodes nto groups wthn whch the network connectons are dense but between whch they are sparser [17]. Ths s shown n Fgure 2. Here the node n bold mark moves from one communty to another and sets up dfferent socal tes wth dfferent nodes present over there. The numbers n the Fgure 2 ndcate how the poston of the node changes wth tme n a communty structure. The socal behavor of a node essentally depends on ts communty behavor.e. the nvolvement of the node to dfferent socal scenaros. The degree of nteracton of a node wthn ts orgnal communty s much more than,

5 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE when t enters a newer communty. For example, a node from a unversty campus may vst a dsaster relef camp. The pedestran moblty pattern for these two locatons where, N = Total no. of socal neghbors above the CT level n a socal network of whch s equal to the number of elements of the row nteracton matrx for the node. From (1) and Tables I & II, we can say that CT approaches a steady state value less than 1. Snce, for a hghly socal node the value of N s very hgh compared to the numercal values of CFs, n that case F also tends to a steady value less than 1. B. Formulaton of Pause Tme Fgure 2. Movement of a node n a Communty Structure. wll be dfferent and wll also nfluence ts socal behavor. In ths context, we defne another parameter called Communty Factor (CF): CF C * NNC where, NNC = New Network Coeffcent whose value s ether 0 or 1 and C = Specfc grade assgned to a partcular socal network e.g. battlefeld, cafetera etc. Here, the term NNC ndcates whether t s exposed to a new network or not. Clearly, for a new network, ts value s 0, snce we do not consder the contrbuton of a new network to the value of CF. Thus for the sad example, the socal behavor of the node n the dsaster relef camp wll depend on the prevous exposure of the node to ths new communty. Wth the help of these factors, we now try to fnd out an ndcator of the atttude of a node towards the nteracton wth others. To ths end, we ntroduce Socal Factor ( F ), whch gves a measure of the degree of nteracton between a node and others present n the adhoc network. For a node, the socal factor ( F ) s gven as: F N j1 j k j N C * CF * CF j (3) (2) We explctly defne Pause Tme (PT) for our moblty model as the tme elapsed by a node when t meets a socal neghbor over a wreless channel or n a geographc locaton n a MANET. As an example, we can say that the dstrbuton of pause tme n the classroom s a bell-shaped normal dstrbuton [10], wth the peak around the mnutes nterval, whch s the regular class duraton. Bascally, the dstrbuton s based on Markov model of locaton transton of moble nodes. However, we try to develop an expresson of pause tme based on our socal factors as gven n Secton IV.A. We do ths because nstead of takng a fxed value of pause tme (as n the case of RWP) or smply some random value, we make pause tme as a functon of socal network parameters. Snce geographc groupng s a dfferent concept to socal groupng, socal attractveness of dfferent groups plays a key factor for controllng pause tme. We defne another quantty namely Prevous Average Connectvty (PAC) whch s the average tme of connecton of node to a socal group G. Thus, assocatng all the varables together (ncludng F ), we gve an emprcal relaton connectng F and PT: PT = F *GA *[1+PAC (t)] (4) where GA s the ndvdual group attracton force of the node to the group G and has a value n the range [0, 1].e. a node may have no pause tme at all. Here, the term PAC (t) also serves as a hstory parameter for dfferent nodes. Table III gves some values of PT for the moble nodes n an ad-hoc network. Thus, nstead of usng random pause tme for the moble users scattered across a socal gatherng, we try to fnd out a node specfc pause tme. TABLE III. SAMPLE VALUES OF PAUSE TIME (PT) Node No. F GA PAC (t)( (sec) sec) P PT (sec) (sec)

6 42 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE 2006 C. Effect of Group Velocty on the Moble Nodes In ths Secton, we defne the followng terms: V n =Velocty of a node wthn a group V g = Velocty of a group Whle V n represents the ndvdual node movement, V g s ndcatve of the average node veloctes wthn a socal group. The effect of the group velocty can be better understood f we consder clusterng n a MANET. In a clustered network, a group of moble nodes communcate wth each other to perform a common task. Here, an analogy can be drawn wth that of a socal groupng n whch there s a drect mpact of the actvty of the group leader on the movement of the nodes. For the sake of clarty, we use the basc relatonshp between the group velocty and the poston of the group members as n [16]. But, here we ntroduce a slght modfcaton that nstead of drect relatonshp between V n and V g, there s also an nfluence of GA, whch s defned n secton IV.B. Hence, the new poston of a moble node, N n after unt tme s gven as: movement of nodes, bouncng off the walls of the obstacles, s unrealstc. People n college campuses or cty terrans do not move about n ths manner, reflectng off buldngs. Thus the movement pattern of the nodes shown n Fgure. 3 does not represent real world stuatons. N n = N p T T Vn Vg dt dt * GA t (5) t 0 0 Fgure 3. Random Obstacle-based Movement. where, N p = Prevous Node poston and T = Total tme elapsed by a node n the present group. It s obvous from (5) that there wll be a tendency for the moble host to change ts present group f a strong group attracton force s exerted on t from an outsde group. Ths s an mportant ssue. Snce, jonng a group or leavng a group s analogous to a new lnk set-up and lnk falure respectvely, and ths moblty pattern of nodes ndcates a necessty for route update for the neghborng nodes. Usng the same relaton, we can also gather nformaton about the socal connectvty of the nodes after a perod of tme. D. Movement of Moble Nodes n presence of Obstacles In order to closely resemble real world stuatons, we ntroduce obstacles n the network area. Unobstructed terrans are unrealstc as real world scenaros contan varous objects placed at varous locatons. The objects act as a barrer to both free movements of moble nodes as well as wreless transmsson between the nodes. These obstacles are used to model buldngs and other structures present n an actual terran lke campus, battlefeld etc. The obstacles can be of varous shapes and szes. For the sake of smplcty, n smulatng our model, we consder regular rectangular shaped obstacles (usng rectangles, varous complex shapes lke L, H can also be constructed) as our smulaton s carred out for a college campus where man obstacles are buldngs whch are usually of regular shapes. The ncorporaton of obstacles, though takes us a step ahead towards accurate modelng of ad-hoc envronments, does not provde a complete soluton. The random When a person travelng towards a destnaton experence an obstacle n hs path, he travels along the edge of the obstacle and then agan contnues n hs desred path. Moreover, people may select specfc buldngs as ther destnatons. Accordngly, n our smulatons (the results of whch have been provded n the next secton), we have provded doors n the obstacles through whch a node may enter or leave. V. SIMULATION RESULTS AND ANALYSIS The prmary objectve of our smulaton s to understand the mpact of socal network consderatons and ncorporaton of obstacles on the moblty dstrbuton of an ad-hoc network whch n turn greatly affects the network performance. To obtan quanttatve nformaton about the proposed moblty model and compare t wth the exstng models, we have smulated our algorthm for an ad-hoc envronment under certan constrants as gven below. We have consdered an ad-hoc network deployed n a unversty campus. The smulaton area s 1000m X 1000m. The maxmum transmsson range of the nodes s consdered to be 250m. The smulaton terran along wth the obstacles present s shown n Fgure 4. The smulaton area has been dvded nto four parts, as shown. Now, 40 moble nodes are placed randomly wthn the area n the followng manner: the nodes are dvded nto four groups of 10 nodes each, each group representng a specfc communty wth ts own partcular communty behavor; the nodes of each group are placed n the four regons of the terran.

7 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE I vj = 1, f the node j s out of range. The ndcator varable for a node s calculated wth all other nodes. The sum of the ndcator varables s equal to the number of neghbors. The average number of neghbors per node s calculated. The smulaton s carred out for half an hour and readngs are taken at regular ntervals of 5 seconds. Further, the exact scenaro s duplcated and smulated once under our proposed model n absence of obstacles and agan under the Random Way-Pont model. The above results show that the ntroducton of obstacles n the smulaton terran largely affects the moblty dstrbuton pattern. Smulatons were also carred out n dfferent scenaros usng the proposed model and also the Random Way-Pont Model n unbounded areas (.e. areas wth no boundares). Fgure 4. Smulated Terran. The nodes are then assgned wth random veloctes rangng from 1 to 4 m/s. The nodes then select ther destnatons, the members of a group tendng to select the same common destnaton. The sngle row nteracton matrces are formed for the varous nodes and the dfferent socal parameters are calculated and after reachng ther desred destnatons, each moble node takes a pause-tme generated usng (4). After pausng for ths tme, t agan contnues ts moton towards some other destnaton. If a node encounters any obstacle n ts path, t follows a path around the obstacle and then agan contnues ts orgnal path, as mentoned n secton IV.D. The nodes may also select ponts nsde the buldngs as ther destnatons, and n that case, t has to enter the buldng through doors stuated on all sdes at the mddle. Average Node Densty Smulaton Tme (n sec) Proposed Model wth Obstacles Proposed Model wthout Obstacles RWP Model Fgure 5. Average Node Densty Vs Smulaton Tme for the campus terran. Now, each node s consdered and the number of neghbors present wthn ts range s calculated. For ths purpose, we use an ndcator varable I vj defned as: I vj = 0, f the node j s wthn the range Percentage Connectvty of Node Smulaton Tme (sec) Proposed Model (Campus) RWP Model Proposed Model (Battlefeld) Fgure 6. Percentage node connectvty Vs Smulaton Tme for dfferent scenaros. Fgure.6 shows a comparson of the proposed model for two scenaros (campus and battlefeld) wth the RWP model. It s evdent from the graph that unlke RWP model, our proposed model s able to capture the tme locaton dependence of moblty dstrbuton for dfferent socal scenaros snce t does not assume random pause tme. Moreover, the degree of connectvty of moble nodes wll suffer a major change for dfferent communtes. Thus, our model reflects the near actual pattern of pedestran moblty dstrbuton. VI. CONCLUSION In ths paper, we have presented a theoretcal framework for the moblty dstrbuton of the nodes n a MANET. Here, we have consdered the effect of socal behavor on the movement of a node whch s bascally a move and pause type of moton. Instead of assumng random pause-tme dstrbuton for the moble hosts, we have desgned a theoretcal background for the pausetme formulaton. The smulaton result of our model shows a marked mprovement over the exstng RWP model regardng the connectvty of nodes. Further, we

8 44 JOURNAL OF NETWORKS, VOL. 1, NO. 2, JUNE 2006 have consdered obstacles n the smulaton terran whch greatly affect node dstrbuton pattern. Moreover, our model has fewer assumptons over the RWP model, thus makng t more realstc. Fnally, we plan to refne our model by determnng the pathways between obstacles and also the transmsson characterstcs n the presence of obstacles, whch are left as future works. REFERENCES [1] T. Camp, J. Boleng, and V. Daves, A survey of moblty models for ad hoc network research, n Wreless Communcaton and Moble Computng Specal Issue on Moble Ad Hoc Networkng: Research, Trends and Applcatons, 2(5): , [2] F. Ba, N. Sadagopan, and A. Helmy, The Important Framework for Analyzng the Impact of Moblty on Performance of Routng for Ad Hoc Networks, Ad-Hoc Networks Journal, Vol. 1, Issue 4, pp , Nov [3] A. Jardosh, E. M. Beldng-Royer, K. C. Almeroth, and S. Sur, Towards Realstc Moblty Models for Moble Ad hoc Networks, n Proceedngs of ACM MobCom, pp , September [4] Chrstan Bettstetter, Govann Resta, and Paolo Sant, The node dstrbuton of the random waypont moblty model for wreless ad hoc networks, IEEE Transactons on Moble Computng, 2(3): , July-September [5] T. Henderson, D. Kotz and I. Abyzov, The Changng Usage of a Mature Campus-wde Wreless Network, n Proceedngs of ACM MobCom, pp , September [6] M. Balaznska and P. Castro, Characterzng Moblty and Network Usage n a Corporate Wreless Local-Area Network, n Proceedngs of MobSys 2003, pp , May [7] M. E. J. Newman, The structure and functon of complex networks, SIAM Revew, 19(1):1 42, [8] X. Hong, M. Gerla, G. Pe, and C.-C. Chang, A group moblty model for ad hoc networks, n Proceedngs of the 2nd Internatonal Workshop on Modelng Analyss and Smulaton of Wreless and Moble Systems, pp , [9] N. Sarshar and R. Chowdhury, Scale-free and stable structures n complex ad hoc networks, Physcal Revew E , [10] Byung-Jae Kwak, Nah-Oak Song, Leonard E. Mller, A Moblty Measure for Moble Ad-Hoc Networks, IEEE Communcatons Letters, vol. 7, no. 8, pp , Aug [11] D. Shukla, Moblty models n ad hoc networks, Master s thess, KReSIT-ITT Bombay, Nov [12] D. S. Tan, S. Zhou, J. Ho, J. S. Mehta, and H. Tanabe, Desgn and evaluaton of an ndvdually smulated moblty model n wreless ad hoc networks, n Proceedngs of Communcaton Networks and Dstrbuted Systems Modelng and Smulaton Conference, San Antono, TX, [13] We-jen Hsu, Kashyap Merchant, Haw-we Shu, Chh-hsn Hsu, Ahmed Helmy, Weghted Waypont Moblty Model and ts Impact on Ad-Hoc Networks, MobCom 2004 Poster Abstract [14] D. J. Watts, Small Worlds the Dynamcs of Networks between Order and Randomness, Prnceton Studes on Complexty. Prnceton Unversty Press, [15] K. Hermann, Modelng the socologcal aspect of moblty n ad hoc networks, n Proceedngs of MSWM 03, San Dego, Calforna, USA, September [16] Mrco Musoles, Stephen Hales, Cecla Mascolo, An Ad Hoc Moblty Model Founded on Socal Network Theory, n Proceedngs of 7 th ACM Internatonal Symposum on Modelng, Analyss and Smulaton of Wreless and Moble Systems, Vence, Italy, pp , [17] M. E. J. Newman and M. Grvan, Fndng and evaluatng communty structure n networks, Phys. Rev. E 69, (2004). P. Venkateswaran s workng as a Reader n the Dept. of Electroncs & Tele-Communcaton Engg. (ETCE), Jadavpur Unversty (JU), Kolkata, Inda. He has publshed over 30 papers n varous Natonal / Internatonal Journal / Conference Proceedngs. Hs felds of nterest are Computer Communcaton, Mcrocomputer Systems and Dgtal Sgnal Processng (DSP). He s a Member of IEEE (USA). Rahul Ghosh s currently pursung hs Bachelors Degree n the Dept. of ETCE, JU. He won the Thrd Prze n the IEEE All Inda M. V. Chauhan Students Paper Contest - MVCSPC He s a member of IEEE Communcatons Socety. Hs areas of nterest are Wreless Communcaton, Computer Networks and Embedded Systems. Artra Das s currently pursung hs Bachelors Degree n the Dept. of ETCE, JU. He won the Thrd Prze n the IEEE All Inda MVCSPC He s a Student member of IEEE. Hs areas of nterest are Wreless Communcaton, Computer Networks and Embedded Systems. Dr. Sall Kumar Sanyal s a Professor n the Dept. of ETCE, JU. He has publshed more than 100 research papers n Internatonal / Natonal Journals / Conference Proceedngs. Hs current research nterests nclude Analog Sgnal Processng (ASP) & DSP, Tunable Mcrostrp Antenna, Communcaton Engneerng, VLSI Crcuts & Systems Desgn. He s the present Charman of IEEE Calcutta Secton. Dr. Rabndranath Nand s a Professor n the Dept. of ETCE, JU. Hs areas of nterest are ASP, DSP, Computer Communcaton. He has authored more than 110 research papers n Natonal / Internatonal Journals and some n Conferences / Semnars. He served as the Head of ETCE Dept., JU durng and served as the Char of IEEE Calcutta Secton durng He has taught n varous Insttutes abroad.

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