Bayesian Model for Mobility Prediction to Support Routing in Mobile Ad-Hoc Networks

Transcription

1 Bayesan Model for Moblty Predcton to Support Routng n Moble Ad-Hoc Networks Tran The Son, Hoa Le Mnh, Graham Sexton, Nauman Aslam, Zabh Ghassemlooy Northumbra Communcatons Research Laboratory (NCRLab Faculty of Engneerng and Envronment Northumbra Unversty, Newcastle Upon Tyne, UK {tran.t.son, hoa.le-mnh, g.sexton, nauman.aslam, z.ghassemlooy}@northumbra.ac.uk Abstract- Ths paper ntroduces a Bayesan model to predct and classfy the moblty of a node n Moble Ad-hoc Networks (MANETs. The proposed model does not use the addtonal nformaton from Global Postonng System (GPS for ts predcton as some exstng models dd. Instead, t reles on the average encounter rate and node degree calculated at each node. However, the outcome s stll recorded at hgh accuracy,.e. predcton error s fewer than 10% at hgh speed level (above 15m/s. The am of ths model s to help a routng protocol n MANETs avod broadcastng request messages from a hgh moblty node/regon reled on the outcome of the predcton. Through smulaton experments, route error rate observed reduced sgnfcantly compared to normal broadcast scheme of the Ad-hoc On-demand Dstance Vector (AODV protocol. The packet delvery rato mproved up to 46.32% at the maxmum velocty of 30m/s (equal to 108km/h n the densty of 200nodes/km 2. Keywords: Moble Ad-hoc Networks, Moblty-aware Routng, Bayesan Classfer, Average Encounter Rate. I- INTRODUCTION A moble ad-hoc network (MANET s a form of wreless networks n whch moble nodes move randomly and communcate to other nodes wthout usng any communcatons nfrastructure. Data packets can be relayed at ntermedate nodes before reachng the destnaton [1], [2]. To send a data packet, the source node needs to establsh a route through other nodes nstead of sendng data over common meda such as cable systems or access ponts. Therefore, the routng scheme n MANETs s dfferent from other networks. One of generc strateges to fnd a route to the destnaton s to broadcast request messages perodcally on the whole network untl the destnaton s reached. The destnaton, f t exsts, reples to the request and the route s establshed. As the nature of MANETs, nodes can move durng transmsson sessons, therefore the establshed lnk could be broken at any tme. Ths ssue presents MANETs under many challenges whle routng a packet [2], [3] across the network. The performance of routng wll become very poor f the moblty of nodes s very hgh. In such crcumstances, a routng protocol wll typcally re-broadcasts request messages to fnd another route to the destnaton. Dependng on the stablty of the establshed lnk, a node can re-broadcast one or more tmes durng transmsson sessons. Ths could lead to the broadcast storm problem [4] under whch a MANET wll be flooded by ts control messages resultng n the reducton of bandwdth for data. Therefore, predcton and awareness of nodes moblty durng probng a request packet s sgnfcant n MANETs. It could mprove the routng performance and reduce floodng problem. So far, several solutons have been proposed to be aware of the moblty whle routng n MANETs. Related works By usng GPS nformaton, the predcton model proposed n [5] has the ablty to predct the topology changes n order to provde the seamless connecton servce for MANETs. In partcular, GPS nformaton s used to estmate the lnk expraton tme (LET between two adjacent nodes. Based on ths predcton, packets wll be re-routed before lnks expre. The paper showed the packet delvery rato mantaned above 90% for all moblty speeds. In an attempt not to use the GPS nformaton, the authors n [6] predcted the moblty of a node that reled on detectng the changes of neghbour vectors n a certan nterval. A routng protocol wll use ths predcton to determne whch path s the most stable and then forward the packet. The authors showed the lnk breaks reduced 25% compared to exstng protocols. By relyng on a metrc named moblty factor (MF to estmate the stablty of a node, the authors n [7], [8] desgned Q-Routng based algorthms [9] to fnd the most stable path when routng a packet over the MANETs. The MF metrc s constructed by observng the changes of neghbour node set before and after expraton tme of a HELLO message. The hgher the MF value s, the more stable the node s. The am of routng protocols s to choose the path whch has the hghest MF value to forward data. Another suggested approach to estmate the moblty of moble nodes s to rely on moblty hstory usng neural networks [10] or Gauss-Markov random process [11]. The accuracy of predcton was very hgh. However, those models are good to use for predctng trajectores of moble nodes rather than routng a packet or broadcastng requests. Snce the predctors n those models take a long tme to learn, they wll cause severe delay when dssemnatng a route request. In general, GPS-based predcton method s one of good solutons to estmate the network moblty. However, GPS mght not be avalable on many devces and many places. The other models n [6], [7], [8] have not explctly shown the relaton between moblty metrcs and the velocty of a node. Addtonally, those models lacked evaluatons for the accuracy of ther predctons. Ths paper ntroduces a non GPS-based model to nfer the moblty of network nodes n MANETs based on node degree /13/$ /13/$ IEEE 3201

2 and the Average Encounter Rate ( whch s a metrc for MANETs routng proposed n [12]. A Bayesan Classfer s then used as an nference system to predct the moblty of a node tself. Though the proposed model does not use addtonal nformaton from GPS, the predcton shows at hgh accuracy. The outcome of Bayesan Classfer wll help a node control ts broadcast process by whch a hgh moblty node or regon s avoded to re-broadcast a request. Establshed routes usng the proposed model are more stable than routes determned by exstng routng strateges. Ths model s a dstrbuted algorthm and ndependent of the moblty pattern. The rest of ths paper s structured as follows. Secton II ntroduces Bayesan Classfer as a moblty estmator to classfy and predct the moblty of a node. Secton III analyses and valdates the predcton s outcome. Secton IV compares routng performances wth and wthout Bayesan Classfer ntegrated to support broadcastng at each node. Fnally, Secton V concludes the paper. II- SYSTEM MODEL Defnton 1 (Encounter Two nodes encounter each other when the dstance between them becomes smaller than the communcaton range R [12]. In ths crcumstance, each node s consdered as a new encounter of the other. The encounter e between node n A and node n B s represented by the tme t at whch 2 nodes meet each other wthn a duraton t. e = { n, n, t, Δt} ( 1 A Defnton 2 (Average Encounter Rate The average encounter rate ( s the average number of new encounters experenced by each node n a duraton T. Let E n be the set of new encounters observed wthn duraton T, the can be calculated as follow [12]: En = ( 2 T where E n s the cardnalty of set E n. Ths paper uses the analyss n [12] for estmaton. Assumng nodes are movng n Random Waypont moblty model wth maxmum velocty of v max, the can be estmated as En = = R vmax d ( 3 T where R s the communcaton radus of each node; d s the densty of the network. A MANET s modelled by a random graph G(V, U, where V s a set of nodes movng wthn an area A and U s a set of lnks between pars of nodes n the graph. A lnk {u, w} from node u to node w appears when node w s comng nto the communcaton range of node u. At ths pont of tme, node w s recognzed as a new encounter of node u and vce versa. Each node s equpped wth a sngle rado wth fxed transmsson range R. The Equaton (3 shows that the velocty of a node can be estmated by tself f s known and the network densty d s gven. B The frst component, can be easly determned by detecton of new neghbours comng nto the communcaton range at each node. The second one, node densty d s unknown because nodes are dstrbuted randomly and move autonomously as the nature of MANETs. However, t can be predcted locally by observng the degree of each node. In a gven graph G(V, U, the degree k of a node whch s also known as the number of ts neghbours has a probablty dstrbuton functon (pdf calculated by [13] n k N k n k N e pk = p (1 p ( 4 k k! where N s the average number of neghbours of each node; n s the total number of nodes n the network; p s the probablty of exstent a lnk between two nodes. Ths dstrbuton s recognzed as the Posson dstrbuton. Fg. 1- Node degree dstrbuton at dfferent denstes The average number of neghbours N can be dentfed reled on average densty of the network as follow: n N d = = ( 5 A 2 πr where n s total number of nodes, A s the area of the network. The relaton between the node degree k and total number of nodes n n the Equaton (4 allows us to estmate the network densty reled on node degree (see Fg. 1 and then predct the velocty of a node based on the Equaton (3. A Bayesan Classfer whch operates as an nference system [14] s ntegrated nto each node to predct the velocty. The nference model has two nput attrbutes (nput varables: and node degree k (see Fg. 2. The possble target values ncludng low, medum, hgh velocty are represented by classfcaton varable v. The classfer wll choose the most probable value among possble values based on nput examples by usng the Maxmum A Posteror (MAP method as follow: v = arg max p( c x, x ( 6 c C By applyng the Bayes theorem we have p( x, xk c p( c v = arg max c C p( x, xk = arg max p( x, x c p( c c C k k (

3 where C = {Low, Medum, Hgh}. Accordng to Bayesan methodology, the outcome of the classfer should be v = arg max c { Low, Medum, Hgh} p( c p( x c p ( x k c (8 It s noted that the equatons of (3, (4 and (5 express a relaton between and node densty k. In other words, the varables of and node densty are not totally ndependent as the expectaton of the Bayesan approach. However, under that crcumstance, the Bayesan Classfer s stll optmal [15] and could gve us a good predcton (seee also analyss n Secton III. as descrbed above. A routng protocol then reles on those estmates to determne whether to re-broadcast the request messages as llustrated n the ffth column of the TABLE 2 (.e. row #3, row #6, row #8 and row #9. TABLE 2 - TABLE OF TRAINING DATA # Node Velocty Rebroadcast degree (estmate 1 Low Low Low Yes 2 Low Medum Medum Yes 3 Low Hgh Hgh No 4 Medum Low Low Yes 5 Medum Medum Medum Yes 6 Medum Hgh Hgh No 7 Hgh Low Medum Yes 8 Hgh Medum Hgh No 9 Hgh Hgh Hgh No III- STATISTICAL ANALYSIS AND EVALUATIONS All experments for analyss and evaluaton the accuracy of the predcton n ths secton are conducted on ns-3 smulator verson 3.16 wth setup parameters descrbed n TABLE 3. Fg. 2- Bayesan Classfer model to predct the node s moblty. From the Bayesan perspectve, all attrbutes ncludng velocty v, average encounter rate and node degree k need to be classfed nto dfferent levels. Supposng that the velocty v s rangng from 0 m/s to 20 m/s and beyond (denoted by 20 +, t s classfed nto low, medum, hgh levels as shown n TABLE 1. Analogcally, the densty d s consderedd from 0 to nodes/m 2 and beyond (denoted by 2* Ths range s correspondent to the populaton of 0 nodes to 200 nodes (and beyond over an area of 1km 2. The node densty d can be categorsed as low, medum, hgh levels lsted n TABLE 1. TABLE 1 CLASSIFICATION TABLE Low Medum Hgh v (m/s 0 < v < v < v 20 + d (nodes/m 2 0 < d 0.5* 10-4 < d 1.5*10-4 < d 0.5* * * < 0.25 < 0.56 < k [0 20 [ Equaton (3 allows us to determne the range of wth respect to velocty s range and node densty levels. The range of and ts levels presented n TABLE 1 are calculated wth communcaton range R=250m. For a real devce, ths range can be derved from ts transmttng power. From the node degree dstrbuton n the Equaton (4 and the average number of neghbours n the Equaton (5, node densty d and ts correspondng node degrees k are dentfed and categorsed (see also Fg. 1. Eventually, the tranng data for Bayesan Classfer s desgned n expectaton of avodng hgh velocty nodes or regons to mnmze the lnk breakages (see TABLE 2. The fourth column of the TABLE 2 contans the estmated veloctes whch are the output values of Bayesan Classfer Fg. 3- vs. node densty and velocty based on (3 To evaluate the accuracy of the predcton, we frstly examne the relaton among, the velocty v of a node and the node densty d shown n Equaton (3. Ths examnaton s also useful for us to calbrate the levels of nput varables (.e. and k and classfcaton varable v of Bayesan Classfer later on. The theoretcal result n Fg. 3 and emprcal results n Fg. 4 confrmed the estmaton n the Equaton (3. Fg. 4 - vs. node densty and velocty. The node degree dstrbutons n Fg. 5 are obtaned at dfferent node denstes,.e. 50 nodes, 100 nodes, 150 nodes and 200 nodes over an area of 1km 2, and ndependent to the velocty. In other words, the node degree dstrbuton s dentcal regardless of the moblty of the network and fts well to the theoretcal curves shown n Fg

4 Fg. 5 - Node degree dstrbuton at dfferent denstes The above analyss and experments enable us to use node degree to locally estmate the densty of the network. Therefore, the Bayesan Classfer model llustrated n Fg. 2 s vald for predctng and classfyng the moblty of a node. The predcton error rato n Fg. 6 whch reflects the accuracy of the proposed model s calculated by countng number of predcton errors n three dfferent velocty levels (low, medum, hgh over the total number of observatons. As the fgure shows, the predcton error ncreases when the moblty of the network ncreases. Ths s due to the fact that a new encounter could come and leave before beng determned as a new encounter. velocty s detected to avod a potental lnk break durng data communcaton. The Bayes AODV s smulated and compared to the orgnal AODV on the ns-3 smulator (see smulaton setup n TABLE 3. To evaluate the routng performance of the Bayes AODV, some performance metrcs below are consdered to use: - Route error rate (RER: the number of route errors occurred n a gven duraton on the whole network. - Packet delvery rato (PDR: the rato of the data packets delvered to the destnatons to those generated by the CBR sources. - Emprcal cumulatve dstrbuton functon (Emprcal CDF of end-to-end throughput: the convergence rato of emprcal CDF of end-to-end throughput over paths. An emprcal CDF at a data rate t (Kbps of end-to-end paths s calculated by the number of paths whch have ther data rate smaller or equal to t over total number of end-to-end paths across all experments. TABLE 3 - SIMULATION SETUP + Area 1000m x 1000 m. + No. of nodes 50, 100, 150, Smulaton tme 240 seconds + No. of traffc sources 20 + Moblty model Random Waypont (pause tme 0 second + Velocty (maxmum 15, 20, 25, 30 m/s + Traffc type CBR, 4packets/second (UDP + Message sze 512 bytes/packet + Physcal Layer: Wf IEEE b, 2.4GHz; Communcaton range 250m. The smulaton results show that at both medum node densty (10-4 nodes/m 2 and hgh node densty (2x10-4 nodes/m 2 the packet delvery rato of the Bayes AODV mproved compared to the orgnal AODV,.e % and 46.32% respectvely (see Fg. 7a. Fg. 6- The predcton errors at dfferent veloctes For example, n a hgh moblty scenaro, f a node s movng at the speed of 30 m/s (equal to 108km/h; the perod of observaton a new encounter at each node s set to 10s; and communcaton radus s 250m, wthn 10s that node could move up to 300m whch s out of the coverage of observng nodes before detectng as a new encounter. Therefore, errors could occur when calculatng at each node resultng n errors n predcton. IV- RESULTS AND DISCUSSIONS The above predcton model s then ntegrated nto the AODV [16] protocol (named Bayes AODV to help the AODV control the broadcast process. In partcular, a request message (RREQ s dened to be re-broadcasted f the hgh Fg. 7 (a Packet delvery rato at two dfferent node denstes (b Route error rate at two dfferent node denstes The Bayes AODV s also recorded nducng less route error rate than the orgnal AODV (Fg. 7b,..e. at hgh densty (2x10-4 nodes/m 2 route error rate under the Bayes AODV s only error/s whch reduced over 80% compared to route error rate under the orgnal AODV. Comparng to solutons n [6], [7] ths s a remarkable enhancement. These results mply that by avodng the hgh moblty nodes durng dscoverng a route to the destnaton, packets under the Bayes AODV are routed over paths whch are more stable than shortest paths under the orgnal AODV. The end- 3204

5 to-end paths under the Bayes AODV are also observed at hgher throughput than paths under the orgnal AODV. Fg. 8 shows that at every CDF rato, the Bayes AODV always offers hgher throughput than the orgnal AODV. Fg. 8 - (a Emprcal CDF recorded at the densty of 10-4 nodes/m2. (b Emprcal CDF recorded at the densty of 2x10-4 nodes/m2. Dscusson One of the man concerns of ths model s related to the observng perod of a new encounter. Ths parameter drectly nfluences to the values calculated at each node, therefore affectng to the accuracy of predcton. In ths model, to detect a new encounter, each node sends probe packets to ts neghbours perodcally. The perod of sendng probe packets s known as observaton perod. If ths perod s short, the accuracy of observaton s hgh. But t generates more probe packets whch could occupy remarkable amount of bandwdth and cause floodng the network. If ths perod s large, a new encounter could come and leave wthout beng counted as a new encounter resultng n naccurate value calculated. Another ssue stems from a partcular scenaro n whch there exsts a unque lnk to the destnaton through hgh moblty node(s. In ths crcumstance, the destnaton mght appear as an unreachable pont though the end-to-end lnk could be establshed and operated at a low qualty. However, our results showed that all destnatons are reachable under the Bayes AODV. V- CONCLUSION In ths paper, we have proposed a model to predct the relatve velocty of a node tself by usng Bayesan Classfer as a predctor. The predcton s based on the nformaton of and node degree whch can be observed and calculated locally at each node. Ths soluton s consdered as a dstrbuted algorthm. The advantage of ths soluton s the fact that t requres no addtonal nformaton from GPS system as other models dd. In spte of that, the predcton results are shown at hgh accuracy. By estmatng the velocty of a node tself, the Bayesan Classfer helps a routng protocol determne whether to rebroadcast a RREQ message. The recorded mprovement of Bayes AODV s 46.32% hgher than orgnal AODV at the hgh densty scenaro (200 nodes/km 2. That s a remarkable enhancement compared to other proposed solutons. Moreover, the manner of detectng a new encounter and computng values at each node as descrbed n ths paper s ndependent to the routng strateges,.e. reactve or proactve; therefore ths model can be deployed on any routng protocol types. ACKNOWLEDGMENT One of the authors, Tran The Son would lke to gratefully acknowledge the fnancal support from Vetnamese Government under Project No. 165 to carry out ths research. REFERENCES [1] R. R. Roy, n Handbook of Moble Ad-hoc Networks for Moblty Models, ISBN , Sprnger, [2] Azzedne Boukerche, Begumhan Turgut, Nevn Aydn, Mohammad Z. 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