Mobility Management and Its Applications in Efficient Broadcasting in Mobile Ad Hoc Networks

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1 Mobilit Management and Its Applications in Efficient Broadcasting in Mobile Ad Hoc Netorks Jie W and Fei Dai Department of Compter Science and Engineering Florida Atlantic Uniersit Boca Raton, FL {jie, fdai}@cse.fa.ed. Abstract We std an efficient broadcast scheme in mobile ad hoc netorks (MANETs). The objectie is to determine a small set of forard nodes to ensre fll coerage. We first std seeral methods to select a small forard node set assming that the neighborhood information can be pdated in a timel manner. Then e consider a general case, here each node pdates its neighborhood information based asnchronosl on a pre-defined freqenc and node moe een dring the broadcast process. The irtal netork constrcted from local ies of nodes ma not be connected, its links ma not eist in the phsical netork, and the global ie constrcted from collection of local ies ma not be consistent. In this paper, e first gie a sfficient condition for connectiit at the phsical netork to ensre the connectiit at the irtal netork. We then propose a soltion sing to transmission ranges to address the link aailabilit isse. The neighborhood information as ell as the forard node set are determined based on a short transmission range hile the broadcast process is done on a long transmission range. The difference beteen these to ranges is based on the pdate freqenc and the speed of node moement. Finall, e propose a mechanism called aggregated local ie to ensre consistenc of the global ie. B these, e etend W and Dai s coerage condition for broadcasting in a netork ith mobile nodes. The simlation std is condcted to ealate the coerage of the proposed scheme. 1 Keords: Broadcasting, localized algorithms, mobile ad hoc netorks (MANETs), mobilit, simlation, sstem design. I. INTRODUCTION Broadcasting a packet to the entire netork is a basic operation and has etensie applications in mobile ad hoc netorks (MANETs). For eample, broadcasting is sed in the rote discoer process in seeral roting protocols, hen adising an error message to erase inalid rotes from the roting table, or as an efficient mechanism for reliable mlticast in a fastmoing MANET. In MANETs ith the promiscos receiing mode, the traditional blind flooding incrs significant redndanc as ell as collision and cases the so-called broadcast storm problem [1]. Efficient broadcasting in a MANET focses on selecting a small forard node set hile ensring broadcast coerage. In a broadcast process, each node decides its forarding stats based on gien neighborhood information, and the corre- 1 This ork as spported in part b NSF grants CCR , ANI , and EIA Fig. 1. Forard node set in a MANET. sponding broadcast protocol is called self-prning. In Figre 1, black (hite) nodes are forard (non-forard) nodes. Each circle corresponds to a one-hop neighborhood. An sorce node is a black node b defalt. Basicall, forard nodes form a connected dominating set (CDS), here each node in the sstem is either in the set or the neighbor of a node in the set. That is, each hite node is adjacent to at least one black neighbor. Hoeer, most eisting broadcast schemes assme either the nderling netork topolog is static or semi-static dring the broadcasting process sch that the neighborhood information can be pdated in a timel manner. The reslts in [2] sho that eisting static netork broadcast schemes perform poorl in terms of delier ratio hen nodes are mobile. There are to sorces that case the failre of message delier: Collision: The message intended for a destination collides ith another message. In Figre 1, if messages from nodes and collide at node, node does not receie an message. Mobile nodes: The neighbor in the neighbor set moes ot of its transmission range (i.e., it is no longer a neighbor). In Figre 1, hen node moes ot of the transmission range of, the nodes along the branch rooted at of the broadcast tree ill miss the message 2. 2 Nodes in the branch ma still receie the message, if some adjacent nodes of the branch forard the message.

2 Reslts in [2] also sho that the majorit of delier failres are cased b mobile nodes. Althogh man broadcast protocols hae been proposed ith different broadcast redndancies (and collated broadcast delier ratios), each broadcast protocol has onl its fied broadcast redndanc (and broadcast delier ratio). It is in general hard to control redndanc and delier for a gien broadcast protocol. The major challenges in designing a localized broadcast protocol hile ensring broadcast coerage are the folloing: (a) The netork topolog changes oer time, een dring the broadcast process. (b) The local (1-hop) information is constrcted based on Hello interals. Nodes start their interals asnchronosl, making it difficlt to ensre consistent local/global ies among nodes. (c) The collection process for k-hop information incrs dela hich ma not reflect the crrent netork topolog hen there are mobile nodes, een for small k in localized soltions. As a conseqence, the irtal netork constrcted from local ies of nodes ma not be connected (connectiit isse), its links ma not eist in the phsical netork (link aailabilit isse), and the global ie constrcted from collection local ies ma not be consistent (consistenc isse). In this paper, e first gie a sfficient condition for connectiit at the phsical netork to ensre the connectiit at the irtal netork. We then propose a soltion sing to transmission ranges to address the link aailabilit isse. The neighborhood information as ell as the forard node set are determined based on a short transmission range hile the broadcast process is done on a long transmission range. The difference beteen these to ranges is based on the pdate freqenc and the speed of node moement. The difference is also sed as a ne controllable parameter to balance broadcast redndanc and broadcast delier ratio. Finall, e propose a mechanism called aggregated local ie to ensre consistenc of the global ie. The simlation std is condcted to ealate the coerage of the proposed scheme. Note that the forarding probabilit in probabilistic broadcasting [1] is also a controllable parameter. Hoeer, it is difficlt to establish a direct connection beteen parameter selection and node mobilit. B proiding soltions to the aboe three isses, e also etend W and Dai s coerage condition [3] for broadcasting in a netork ith mobile nodes. This coerage condition is a sfficient condition for a node to determine its non-forard stats based on k-hop neighborhood information (for small k, sa 2 or 3) onl. Hoeer, the coerage condition as onl sitable hen the topolog is static dring the broadcast process and neighborhood information is consistent ith the crrent state. Simlation reslts in this paper sho that the proposed scheme improes the coerage significantl. The main contribtions of this paper are as follos: 1) Propose the first localized broadcast protocol that can handle mobilit hile ensring broadcast coerage. 2) Sstematicall address the isse of inconsistent local ie cased b neighborhood information dela, asnchronos Hello interals, and node mobilit. 3) Introdce a ne controllable parameter to balance broadcast efficienc and broadcast delier ratio. 4) Condct a comprehensie simlation on the ne approach, comparing ith eisting methods. The remainder of the paper is organized as follos: Section II proides some preliminaries and related orks, especiall W and Dai s coerage condition. Section III proposes the mobilit control method based on to transmission ranges, and gies some analtical std and optimization techniqes. Simlation reslts are presented in Section IV. The paper concldes in Section V. II. PRELIMINARIES AND RELATED WORKS This section starts ith some related ork on mobilit management and, in particlar, neighbor set management in a mobile enironment. Then an oerie of broadcast protocols in MANETs based on self-prning is gien. The focs is on W and Dai s coerage condition and si eisting protocols as its special cases. A. Mobilit management The capacit of MANETs is constrained b the mtal interference of concrrent transmissions beteen nodes. The mobilit of nodes adds another dimension of compleit in the mtal interference. Seeral stdies [4], [5] focsed the effect of mobilit on the netork capacit. Camp et al [6] gae an ecellent sre on mobilit models for MANETs. Three poplar mobilit models inclde (1) random alk, hich is a simple mobilit model based on random directions and speeds, (2) random apoint, hich incldes pase time beteen changes in destination and speed, and (3) random direction mobilit, hich forces hosts to trael to the edge of the simlation area before changing direction and speed. In [7], a elocit-bonded model (for pedestrians ith mobile nodes in a relatiel small area), and an acceleration-bonded model (for ehicles of high speed) are gien. Other mobilit models are discssed in [7], and their impact on performance of roting protocols is discssed in [8]. Ver little ork has been done in maintaining an accrate neighbor set in MANETs. One eception is [9], here a stable zone and a cation zone of each node hae been defined based on a node s position, speed, and direction information obtained from GPS. Specificall, stable zone is the area in hich a mobile node can maintain a relatiel stable link ith its neighbor nodes since the are located close to each other. Cation zone is the area in hich a node can maintain an nstable link ith its neighbor nodes since the are relatiel far from each other. The draback of this approach is that it is GPS-based, hich comes ith a cost. In addition, there is no rigoros analsis on the impact of mobilit on the selection of these to zones. Seeral papers [10] address the isse of the length of time that to nodes ill remain close enogh in proimit for a link beteen them to remain actie. Seeral roting protocols, associatiit-based roting (ABR) [11] and signal stabilitbased adaptie roting (SSA) [12], hae been proposed that

3 select stable links to constrct a rote. In [13], GPS information is sed to estimate the epiration time of the link beteen to adjacent hosts. Recentl, seeral stdies hae been done on the effect of mobilit on roting path [14]. Hoeer, no broadcast protocol ses the notion of stable link to ealate the stabilit of neighbor set in order to better decide the forarding stats of each node. Althogh seeral probabilistic broadcast protocols [1], [15] hae been proposed b trading beteen efficienc (simple design) and coerage (delier ratio), it is difficlt to establish a direct connection beteen forarding probabilit and node mobilit. B. Broadcast protocols based on self-prning W and Dai [3] proposed a generic scheme that coers most eisting self-prning protocols. In the generic self-prning scheme, each node bilds its k-hop information b echanging (k 1)-hop information ith its neighbors ia periodical Hello messages. Here e define the k-hop neighbor set N k () of node as the set of nodes that is at most k hops aa from, and the eact k-hop neighbor set H k () as the set of nodes that is eactl k-hops aa from. That is, N k () =H 1 () H 2 ()... H k (). Thek-hop information of a node contains the topolog information that can be collected ia k ronds of Hello message echanges, inclding nodes in N k (), links among nodes in N k 1 (), and links beteen H k 1 () and H k (). For eample, links beteen to nodes eactl 2 hops aa are inclded in 3- hop information, bt not in 2-hop information. The Hello messages also propagate the priorit of each node, hich cold be a permanent propert (e.g., node id) or a dnamic one (e.g., node degree). Dring a broadcast process, each node ma also etract from the incoming broadcast packets a list of isited nodes that hae forarded the same broadcast packet. Using the k-hop topolog, priorit, and isited node information, each node decides its on stats (forarding/non-forarding) based on the folloing coerage condition. Coerage Condition [3]: Node has a non-forard node stats if for an to neighbors and, a replacement path eists that connects and ia seeral intermediate nodes (if an) ith either higher priorit ales than the priorit ale of or ith isited node stats. Assme node id is sed as priorit, node in Figre 2 (a) is a non-forard node based on the coerage condition, becase its neighbors, and, are connected ia a replacement path that contains onl intermediate nodes (in this case, ) ith higher node id than, hile node is a forard node, becase no sch replacement path eists. It as proed in [3] that the coerage condition ensres the coerage; that is, the forard nodes, inclding the sorce, form a CDS and, therefore, the delier of the broadcast packet to eer node is garanteed in a connected netork, gien that no packet is lost de to node mobilit or MAC laer collision. (a) Fig. 2. (a) Forard node set ithot histor information (static). (b) Forard node set ith pstream histor information (dnamic) ith node being the sorce (isited node). A self-prning protocol is static if it does not se isited node in the replacement path; otherise, it is dnamic protocol. In a static protocol, the CDS is constrcted before the broadcasting process starts and, hence, is sorce independent. Dnamic protocols are sorce dependent and sall hae loer broadcast redndanc. For eample, node in Figre 2 (a) is a forard node in a static protocol, as there is no node ith higher priorit that connects neighbors and. When node isses a broadcasting, the broadcast packet is sent three times b nodes, and. In Figre 2 (b), the forard node stats of each node is determined dring a broadcast process, and the pstream histor information is piggbacked ith the broadcast packet. Becase nodes (sorce) and are isited nodes, node can conclde that it can be a non-forard node since to of its neighbors can be connected sing node (a isited node). The broadcast packet is sent tice in the dnamic protocol, one feer than in the static protocol. In [3], it is assmed that local ies of the broadcast specific information (i.e., isited node information) are dnamic bt safe, i.e., an nisited node ill not be mislabelled as isited, and those of the broadcast independent information (i.e., k- hop information and priorit) are static and accrate dring a broadcast process. Hoeer, in mobile netorks, the static information sall changes and cases inaccrate local ies. Based on these inaccrate ies, fll coerage (i.e., 100% delier ratio) is not garanteed. The broadcast redndanc and delier ratio of a self-prning protocol in a mobile enironment is affected b arios implementation options, inclding: Priorit tpe: Each node is associated ith a priorit sed to break a tie in replacement. Using node id as priorit has higher redndanc than node degree (node id is sed then if there is a tie in node degrees) in relatiel sparse netorks. On the other hand, sing node id as priorit has higher delier ratio than node degree in mobile netorks. Node id also has less redndanc in dense netorks. Hello interal: Using smaller Hello interal can proide fresher neighborhood information and improe the delier ratio in a highl mobile enironment. Hoeer, small Hello interals can onl redce, bt not eliminate, ndetected topolog changes. Frthermore, if Hello interal is too short, the oerall broadcasting cost can be higher than flooding (i.e., the (b)

4 Percentage of Forard Nodes (%) Aerage speed = 1 m/s SBA Rles 1&2 Span Rles k LENWB Stojmenoic Generic Nmber of Nodes in Netork Bffer zone Fig. 4. Forard node selection and forarding process based on to different transmission ranges: r 1 and r 2. r2 r1 Delier Ratio (%) (a) Broadcast redndanc erss netork size 100 nodes Flooding SBA 75 Rles 1&2 Span 70 Rles k LENWB 65 Stojmenoic Generic Fig. 3. Aerage moing speed (m/s) (b) Delier ratio erss mobilit Performance of arios broadcast protocols. netork is flooded ith Hello messages). Backoff dela: Dnamic protocols se isited node information to redce broadcast redndanc. A random backoff dela, the time beteen the first receipt of the broadcast packet and the forarding decision, can be sed to discoer more isited nodes and frther increase self-prning efficienc. In some protocols like SBA [16], sing a large backoff dela is essential for the broadcast efficienc. Hoeer, a large backoff dela also cases large end-to-end dela. A random jitter dela is also sed b each node to aoid collision, bt is sall too short to affect the broadcast redndanc or delier ratio. Location information: A protocol sing location information obtained from a GPS deice has smaller Hello messages and fresher neighborhood information than other protocols [17]. On the other hand, GPS deices case etra cost and energ consmption. Location information obtained ma be inaccrate. In addition, neighbor set based on distance (from GPS) ma not be reliable, since it is ell knon that the time ariation of the channel strength can be de to man other factors inclding mltipath fading, shadoing b obstacles, and interference from other sers. Si eisting algorithms, inclding static and dnamic protocols, ere shon to be special cases of the coerage condition. The are: W and Li s marking process ith Rles 1 & 2 (static) [18], Dai and W s Rle k (static) [19], Chen et al s Span (static) [20], Scec and Marsic s LENWB (dnamic) [21], Peng and L s SBA (dnamic) [16], and Stojmenoic s algorithm (hbrid) [17]. Details of these algorithms are gien in Appendi. As shon in Figre 3, high delier ratio can be achieed b protocols ith high broadcast redndanc, i.e., blind flooding, SBA, and Rles 1&2. The ne protocol (labeled as Generic) has the loest redndanc, bt sffers from lo delier ratio in highl mobile netorks. One soltion is to se location information as in Stojmenoic s algorithm, hich achiees higher delier ratio ith relatiel lo redndanc. Hoeer, sing location information incrs etra cost and ma not proide accrate prediction on the eistence of ireless links. SBA achiees er high delier ratio in highl mobile netorks, bt it also has the highest percentage of forard nodes. Note that the percentage of forard nodes in SBA is a fnction of its backoff dela. In netorks ith relatiel lo mobilit, a longer backoff dela can be sed to improe the efficienc of SBA. Hoeer, this also incrs longer end-toend dela, hich is ndesirable nder certain circmstances, e.g., in rote discoer and in applications ith highl mobile nodes. III. PROPOSED METHOD This section proposes a mobilit control method that addresses connectiit, link aailabilit, and consistenc isses. To sfficient conditions, one on the connectiit of the phsical netork that ensres connectiit of the irtal netork and the other on the bond of the range difference that ensres link aailabilit, are gien. Then e introdce methods to rela these sfficient conditions based on probabilistic analsis and optimization techniqes.

5 A. Basic Idea We propose a mobilit management method ithot resorting to location information. This approach is based on to transmission ranges, r 1 and r 2, ith r 1 <r 2. r 1 is sed to collect neighbor set and k-hop information throgh Hello messages, hereas r 2 is sed to perform actal transmission. Specificall, the proposed method consists of to stages: (a) forard node selection, folloed b (b) forarding process. Assme the first stage is done dnamicall dring the broadcast process. Forard node selection: Select a small forard node set sing an eisting method here each neighbor set is based on transmission range r 1. Forarding process: Wheneer a node receies a message for the first time, if it is a forard node, it forards the message sing transmission range r 2. W & Dai s Coerage Condition local broadcast state "Hello" message application Broadcast State (space ie) Logical Netork (time space ie) Phsical Netork transmissions (logical to logical) transmissions (logical to phsical) A node that is ithin the range of r 1 of node is called a neighbor of and the collection of sch nodes is the neighbor set of. The set of nodes that are reachable based on r 2 is called effectie neighbor set. Figre 4 shos the relationship beteen these to transmission ranges. In this eample, is in s neighbor set (also in s effectie neighbor set), hereas is in s effectie neighbor set (bt not in s neighbor set). The idea of to transmission ranges is to se the ring, the area bonded b to circles ith transmission ranges r 1 and r 2, as a bffer zone to nllif the arios bad effects cased b node mobilit and transmission dela. Hoeer, one bad effect called inconsistent local ies cannot be nllified no matter ho ide the bffer zone is. Inconsistent local ies ltimatel reslt in bad decision from a node. A decision is bad if a node that shold forard the message decides on a non-forarding stats. B. Phsical and logical netorks and broadcast states In [3], the coerage condition as applied on a static or semi-static phsical netork. That is, the phsical topolog stops to change seeral Hello interals before a broadcast process, and stas nchanged ntil the broadcast process completes. For the sake of clarit, e assme node id is sed as priorit, and define the local ie of each node as a sbgraph of the phsical topolog (i.e, k-hop information). The correctness of the coerage condition is based on the assmption that eer node decides its forarding/non-forarding stats based on a fresh ie. In MANETs, hoeer, this assmption can be easil iolated de to the continos mobilit. In fact, in order to appl the coerage condition on MANETs ith potentiall obsolete local ies, e introdce the concepts of logical netork and broadcast state. As shon in Figre 5. A logical netork is the collection of all local ies, i.e., a sper graph containing all the nodes and links in local ies. Note that the logical netork is dnamic in a MANET. When the phsical topolog changes, the change is detected b Hello messages and reflected in the logical netork. Fig. 5. The mapping from the logical netork and broadcast state to the phsical netork. Broadcast state, defined as follos, is a snapshot of local ies. For a specific broadcast process, broadcast state forms a irtal static netork, pon hich the coerage condition is applied. Definition 1: A local broadcast state for a broadcast is a local ie at the time the forarding/non-forarding decision is made at an indiidal node. A (global) broadcast state is the collection of all local broadcast states for a specific broadcast. We assme that each node has the same Hello interal f 3, bt each node starts its period asnchronosl. In order to bild k-hop information, each node adertises its (k 1)- hop information ia Hello messages. Each node pdates its local ie based on receied Hello messages. Becase of asnchronos periodic echanges among neighboring nodes, the 1-hop neighbor set in a local ie at a particlar time t does not reflect the actal neighbor set at time t, btthe offset is bonded b the Hello interal f. In fact, k-hop information is a set that consists of neighborhood information sampled at different times. In general, H i+1 () as sampled one interal after H i () for i = 1, 2,..., k 1. Clearl, the k-hop information at time t does not reflect the actal neighborhood topolog at time t, and the offset is bonded b kf. Sppose the speed of node moement is pper bonded b s. Then sf is the maimm distance a node can moe arond dring a Hello interal. The maimm relatie distance beteen to nodes in sch an interal is =2sf. Consider the MANET in Figre 2 (a) and a broadcast process, hich is first from to,, and then from to,, Figre 6 (a) shos the pdate of local ies. We label 3 The condition can also be be relaed in a controllable a, sch as (1 ± 0.25)f in AODV.

6 the time each node sends its last Hello message before the broadcasting as t i, and the time for preios Hello messages as t i 1,t i 2, and so on. Note that t i at each node ma refer to different phsical time. Here each node bilds 2- hop information. If node s Hello message is first receied b node beteen t i 2 and t i 1 (the Hello message propagation is shon in a dotted arro line), it is added to s 1-hop neighbor set, hich is adertised in s net Hello message at t i 1. That is, link (, ) is added to local ies of nodes and. Similarl, link (, ) is also detected and added to local ies of nodes and. Recall in self-prning, each node follos three steps: (a) first receipt of broadcast message, (b) backoff dela, and (c) forard/non-forard stats decision and transmission (if needed). A broadcast period starts from the sorce sending ot the message and ends ith the last node deciding its forarding stats. Like [3], it is assmed that the broadcast message propagates qickl and its dela can be ignored. Backoff at intermediate nodes are alloed, bt accmlatie backoff along each path of the broadcast tree is bonded b b, called broadcast dela, for each broadcast. Note that b ma also inclde broadcast message propagation dela if sch dela cannot be neglected. In Figre 6 (a), the time that each indiidal node makes its decision is marked ith a black dot. Note that local broadcast states are taken at the times marked b these black dots, and the global broadcast state is the collection of local broadcast states (marked b the dashed line connecting all black dots). C. Proposed Methods W and Dai s coerage conditions can be applied to the global broadcast state and ensres coerage, gien that the folloing three conditions are met: Connectiit: The irtal netork that corresponds to the global broadcast state shold be connected in order to appl W and Dai s condition. The folloing theorem shos the densit reqirement at the phsical netork for ensring a connected irtal netork. Theorem 1: If the phsical netork ith transmission range r 1 is connected nder all time, here =2s(f + b), then eer irtal netork indced from a global broadcast state is connected. Proof: Assme the global broadcast state is taken in a broadcast process started at time t. Since the maimm broadcast dela is b, all local states are taken ithin time period [t, t + b]. If the distance of to nodes and, d(, ) r 1 2s(f + b) at time t f, then d(, ) r 1 dring [t f,t+b]. Sppose takes its local broadcast state at t [t, t+b], it mst hae receied at s last Hello message in [t f,t ]. Therefore, link (, ) eists in s local broadcast state. Since the global broadcast state consists of all links from local broadcast state, and the netork is connected at time t f in the range of r 1, the corresponding irtal netork indced from the global broadcast state is also connected. t i 2 t i 2 t i 2 t t (1) i 1 t i i+1 (3) t i 2 t i 1 "Hello" message t i 1 data transmission local broadcast state global broadcast state f t i 1 t i t i 1 t i (a) (1) t i t i (2) (2) (4) (3) (b) backoff period time Fig. 6. The time-space ie of the logical netork of Figre 2 (a) space ie of an inconsistent global broadcast state, after node is identified b node as its ne neighbor (b). Theorem 1 poses a rather strict connectiit reqirement on the phsical netork. That is, if the phsical netork cannot meet the connectiit reqirement, the irtal netork is not garanteed to be connected and W and Dai s approach ill fail. We ill discss later an approach that relaes the connectiit reqirement nder the cost of prning efficienc. Link aailabilit: An link in the global broadcast state shold still eist in the phsical netork dring the broadcast period (i.e., a neighbor sampled ith range r 1 is still a neighbor in the range of r 2 dring the broadcast period). Theorem 2: To ensre the link aailabilit reqirement, r 2 shold be set so that r 2 r 1, here = k + and k for k-hop information. Proof: (sketch) We need to sho that an neighbor nder the transmission range r 1 hen its state is sampled is still an effectie neighbor nder the transmission range r 2 hen the message is sent ot. The total dela incldes k-hop neighbor set collection that takes k interals, and (f + b) broadcast and snchronization dela. The former contribtes a distance of k and the latter. The aboe analsis proides some theoretical fondations for ensring fll coerage. Hoeer, the analsis shos onl the orst case sitation, hich rarel occrs. Later e ill sho that een hen r 2 r 1 is mch smaller than,the probabilit of a ndetected link failre is er lo. Since most (4)

7 moement >r1, <r2 >r1, <r2 moement >r2 s (a) "Hello" range r1 cases partition <r2 s (b) "Hello" range r2 cases link failre (a) (b) (c) Fig. 8. A netork ith one mobile node (a) before the moement and (b) after the moement. Dotted lines represent ndetected phsical links. The dashed line represents a ndetected broken link. Fig. 7. The phsical netork changes from (a) to (b). (c) collection of aggregated local states. self-prning protocols hae certain degrees of redndanc, it sall takes seeral ndetected link failres to fail a broadcast. That is, the probabilit is high that fll coerage can be achieed ith a relatiel small bffer zone idth. There is a ide range of potential tradeoffs beteen broadcast efficienc and broadcast delier ratio. Consistenc: To local ies of nodes and are inconsistent, if there eits a link (, ) in s k-hop information, bt does not ie as a 1-hop neighbor. For eample, assme the phsical topolog in Figre 2 changes shortl before the broadcast. The broadcast ma fail de to inconsistent ies. Figre 7 (a) shos the phsical netork before the change, here node is a non-forard node becase its neighbors and are connected ia a replacement path (,, ). Figre 7 (b) shos the phsical netork before the broadcast, here is a non-forard node becase is no longer a neighbor, and the remaining to neighbors and are directl connected. Node detects the broken link (, ) before node, since is adjacent to the link hile is 2-hop aa from the link. Both nodes ma take a non-forarding stats in the broadcast, s decision based on the otdated ie and s based on the pdated ie. Therefore, node ma neer receie the broadcast packet. We propose to se the aggregated local state to address the inconsistenc problem. The main problem of the aboe eample is that node remoes link (, ) in its local ie before node does so. Note that an broken link is detected first as the loss of a 1-hop neighbor b the end nodes. This link is not remoed from local ies of other nodes ntil the link failre is adertised ia Hello messages. When k- hop information is sed, it takes p to k Hello interals for all related nodes to pdate their local ies. The soltion is that once a node adertises its 1-hop neighbor set, it cannot back aa from it immediatel. That is, each node keeps k recent ersions of N() adertised in its last k Hello messages. The local state sed to make the forarding/nonforarding decision in a broadcast is the aggregation of the k adertised local ies. The aggregation takes 1-hop neighbors from all k ies, bt other information from the last ie onl. The rationale is that node still ies node as its 1-hop neighbor ntil link (, ) is remoed from local ies of all nodes in N k () N k (). Figre 7 (c) shos the collection of aggregated local ies. In this case, node ill still forard. Intitiel, once a node appears as a neighbor of (in the range of r 1 ) dring the recent k interals, it still has to be treated as a neighbor een if it crrentl moes ot of s isible range, bt is still in s effectie neighbor set (as shon in Theorem 2). Another form of inconsistenc might occr if a node ses the Hello message from sent after made its decision (forarding/non-forarding). As shon in Figre 6 (b), node is initiall a neighbor of and later moes to as its neighbor. If Hello message is sent from to after has made its decision, bt before made its, then s decision is made based pon information that is not aailable to hen it made its decision. Consider the folloing seqence of eents as shon in the Figres 6 (a) and (b): (1) decides its nonforarding stats, (2) is detected b as a ne neighbor, (3) adertises its ne neighbor set, and (4) beliees that is coered b and becomes a non-forard node. In this case, ill neer receie the broadcast packet. A simple soltion is for each node that has made a decision on a broadcasting to piggback broadcast id (hich is a tple of sorce id and seqence nmber) and timestamp (the time the decision is made) to the Hello message. The receier can then ignore the Hello message of a sender sent after the decision is made at the sender. Note that the broadcast period is bonded b b; onl recent broadcast id s ithin b need to be piggbacked into the Hello message. D. Implementation Details According to Theorem 1, fll coerage is garanteed onl hen the netork is dense enogh. In the folloing, e propose a mechanism that relaes the connectiit reqirement nder the cost of prning efficienc. In sparse netorks, sing a small Hello transmission range ma case partition in the logical netork. As shon in Figre 8 (a), hen the Hello transmission range is r 1, neither node nor ie node as a neighbor, becase the cannot receie Hello messages from. Therefore, both and become non-forard nodes, and node ill not receie the broadcast packet. Simpl increasing the Hello transmission range to r 2 cannot sole the problem. Since there is no more bffer zone that tolerates node before a topolog change is detected and propagated to the neighborhood. As shon in Figre 8 (b), becomes

8 a non-forard node, reling on to forard the packet. Meanhile, node moes ot of the transmission range of and ill not receie the packet from either. Here e hae a dilemma on the maimal distance beteen to neighbors in the logical netork. If to nodes are ieed as neighbors onl hen their distance is less than r 1, the broadcast ma fail de to partition. If to nodes ith distance larger than r 1 are ieed as neighbors, the broadcast ma fail de to the lack of bffer zone. Or soltion is based on maintaining to neighbor sets. The coered neighbor set, N c (), of node consists of all nodes ithin the normal (large) transmission r 2, and the adertised neighbor set, N a (), consists of onl nodes ith distance less than r 1.If is a non-forard node, eer pair of nodes in N c () mst be connected ia a replacement path. In this case, node in Figre 8 (a) ies as a neighbor and becomes a forard node. On the other hand, onl N a () is propagated to neighbors to bild their k-hop information. Therefore, link (, ) in Figre 8 (b) is inisible to node. Node also forards the broadcast packet and ensres the coerage. Note that this method is conseratie. If link (, ) is still aailable, making node a forard node cases etra redndanc. The dal neighbor sets are constrcted ia sing to Hello transmission ranges: the normal transmission range r 2 and the redced transmission range r 1. This mechanism can be frther improed, if each node can estimate its distance to a neighbor based on Hello signal strength. In this case, Hello messages are sent ia the normal transmission range r 2. Each node constrcts its coered and adertised neighbor sets based on the estimated distances. E. Analtical Std Based on Theorem 2, in order to garantee that a neighbor (ithin r 1 )att 0 is an effectie neighbor (ithin r 2 ) at a time t 1 = t 0 + f, r 1 mst be smaller than r 2 2sf for a gien maimal node speed s and time period f. In this section, e sho that the probabilit, p, that a node ithin r 1 at t 0 moes ot of range r 2 at t 1 is reasonabl small ith a mch larger r 1. We assme a mobilit model similar to the random direction model [22], here each node is moing at a random speed in [0,s] to a random direction in [0, 2π]. This is a simplified model for ease of probabilistic analsis. In addition, this model sall represents the orst case in terms of relatie distance beteen to nodes in a gien interal. Consider to neighboring nodes and (as shon in Figre 9). Node is ithin s Hello transmission range (the shadoed area) at time t 0, and moes to position at t 1. Assme that their distance at t 0 is d, and moes a distance of ith respect to at t 1. The probabilit that moes ot of the normal transmission range of is p(, d) = here 0 : <r 2 d 1 α π : r 2 d r 2 + d 1 : >r 2 + d α =cos 1 ( 2 + d 2 r2 2 ) 2d (1) S1 r1 d a r2 Fig. 9. Calclation of the probabilit that a neighbor ithin the Hello transmission range (r 1 ) moes ot of the normal transmission range (r 2 ). is the largest ale of that satisfies d(, ) r 2. The probabilit that an node ithin the Hello transmission range of moes ot of its normal transmission range at t 1 is here p() = r1 0 2πd S 1 p(, d)dd = S 1 = πr 2 1 r1 0 2d r1 2 p(, d)dd (2) is the area ithin the Hello transmission range. The probabilit that a node ith an constant relatie speed ith respect to moes ot of the normal transmission range is p = 2s 0 f V () p(f)d (3) Here V = V V is the random joint mobilit ector beteen an to mobile nodes and, here V ( V )isthe random mobilit ector of node (). Note that eqation (1) still holds, as the direction of V is also niforml distribted in [0, 2π], and is independent of the speed of V, V. We kno that V is beteen 0 and 2s; V =0hen V = V, and V =0hen V = V and V = V = s. Hoeer, its probabilit fnction, f V (t), is nknon. McDonald and Znati [23] condcted a probabilistic analsis on the joint mobilit of to nodes, bt their analsis is based on the random alk mobilit model [6], here the mobilit ector of each node is the sm of seeral epochs, each epoch has different speed, direction, and dration. Li, Ho and Sha s analsis [24] is based on the same mobilit model as ors, bt their analsis is simplified b the implicit assmption that node is fied and V is niforml distribted in [0,s]. Here e calclate f V (t) at a gien t as f V (t) F V (t + δt) F V (t) (4) δt = P (t V t + δt) δt (2π,s) (2π,s) R( V =, V,t,t+ δt) (2πs) 2 dv δt dv (0,0) (0,0) here F V (t) is the distribtion fnction, δt is a small positie ale, and { R( V, V 1 : a V V,a,b)= b 0 : otherise

9 Probabilit Densit s = 1m/s Velocit (m/s) TABLE I SIMULATION PARAMETERS Parameter Vale Netork area m 2 Nmber of nodes 50, 100 Aerage moing speed m/s Pase Time 0 s Normal transmission range 250 m Hello transmission range m Hello interal s Priorit tpe node id Backoff dela N/A Location information N/A Simlation time 100 s Nmber of trials 20 Confidence leel 95% Neighbor Loss Probabilit (%) (a) The probabilit fnction f V (t) of the random joint mobilit ector r2 = 250m r1 = 250m r1 = 200m r1 = 150m r1 = 100m Velocit (m/s) (b) The probabilit that a neighbor ithin a gien Hello transmission range r 1 moes ot of the normal transmission range r 2. Fig. 10. Calclation reslts. Figre 10 (a) shos the distribtion of V calclated from (4), hen s = 1m/s and δt = 0.001m/s. Note that the probabilit that V > 1.5s is small ( 5%).Basedonthis distribtion, e calclate the probabilit p that an node ithin the Hello transmission range (r 1 = 100, 150, 200, and 250) of moes ot of its normal transmission range (r 2 = 250m) dring a Hello interal (f =1s), hen the maimal single node speed s aries from 0 to 160m/s. Asshonin Figre 10 (b), e can se an r 1 that is mch larger than r 2 2sf, and still epect a lo probabilit that an effectie neighbor moes ot of the normal transmission range. For eample, hen r 1 = 200m and s =80m/s, the probabilit of losing an effectie neighbor is less than 5%. Note that the corresponding r 1 that garantees the aailabilit of link (, ) at time t 1 is r 2 2sf =90m. When r 1 = 100m and s = 160m/s, the probabilit of losing an effectie neighbor is abot the same. On the other hand, there is no r 1 that can garantee the link aailabilit, as 2sf = 320m >r 2. IV. SIMULATION Simlations are condcted to ealate the proposed method and eplore appropriate Hello transmission ranges that achiee high delier ratio ith lo broadcast redndanc nder arios mobilit leels. We also ealate the effectieness of to implementation options that se dal neighbor sets to improe the delier ratio nder arios enironments. A. Simlation enironment The proposed mobilit management method is simlated on ns-2(1b7a) [25] and its CMU ireless etension. We etend the W and Dai s coerage condition b sing to transmission ranges r 1 (for Hello messages) and r 2 (for actal transmission). When r 1 = r 2, the ne algorithm is eqialent to the original generic self-prning protocol. We also simlate the dal neighbor sets enhancement for sparse netorks. The configration of mobile netorks and the implementation parameters of the etended coerage condition are listed in Table I. Since or prpose is to obsere the behaior of self-prning protocols nder mobile enironments, all simlations se an ideal MAC laer ithot contention or collision. If a node sends a packet, all neighbors ithin its transmission range ill receie this packet after a short propagation dela. We assme that accrate location information is either naailable, or nable to predict the eistence of ireless links de to the irreglar ariation of transmission range. It as shon in [2] that the contribtion of a backoff dela to the protocol efficienc is triial ecept for SBA. Therefore, or implementation of the proposed method does not se a backoff dela. The mobilit model sed in the simlation is the random direction model [22]. In this model, each node heads in a random direction and moes at a random speed ntil it reaches the bondar of the area, here it selects ne direction and speed and keeps moing. Or mobilit pattern generator is from [6], hich has a parameter called aerage moing speed (V ag ). For a gien V ag, the speed of each node is randoml selected from the range [0, 2V ag ]. Note that the random direction model sall ields sparser netorks and higher mobilit than the commonl sed random apoint model [6]. Therefore, a reliable protocol in this simlation std is

10 Delier Ratio (%) m 50m 75 20m 10m 0m Aerage Moing Speed (m/s) Delier Ratio (%) m 50m 0m Aerage Moing Speed (m/s) (a) Delier ratio. (a) The original single neighbor set method. Percentage of Forard Nodes (%) Aerage Moing Speed (m/s) 100m 50m 20m 10m 0m Delier Ratio (%) m, signal strength 55 50m, signal strength 50 0m, signal strength Aerage Moing Speed (m/s) (b) Broadcast redndanc. (b) The dal neighbor set enhancement. Fig. 11. Simlations in relatiel dense (100 nodes) netorks. Fig. 12. Delier ratio in relatiel sparse (50 nodes) netorks. a reliable protocol nder the random apoint model, bt not ice ersa. B. Simlation reslts Figre 11 shos simlation reslts in relatiel dense netorks (100 nodes), ith bffer zone idth (i.e., r 2 r 1 ) aring from 0m to 100m. As epected, high delier ratio ( 98%) can be achieed ith large bffer zone idth (100m) in highl mobile netorks (ith aerage speed 160m/s). The onl problem is the high broadcast redndanc ( 60% forard nodes). If the netork mobilit leel is knon, e can select the bffer zone idth based on the mobilit leel to balance the delier ratio and redndanc. For eample, at aerage speed 120m/s, e can se a bffer zone idth of 50m, hich achiees 95% delier ratio ith 40% forard nodes. At aerage speed 40m/s, a10m bffer zone achiees the same delier ratio ith onl 30% forard nodes. Figre 12 (a) shos the delier ratio of the proposed method in relatiel sparse netorks (50 nodes). When a 0m bffer zone is sed, the delier drops rapidl as the aerage speed increases. Using a larger bffer zone idth (50m or 100m) improes the delier ratio nder high mobilit leel, bt performs poorl nder lo mobilit leel. The delier ratio is lo (85% and 70%), een ith triial mobilit (1m/s). One reason for the lo delier ratio in sparse netorks is the relatiel lo redndanc. Simlation reslts in [2] shoed that all self-prning protocols hae loer delier ratio in sparse netorks than in dense netorks nder the same mobilit leel. Another reason is that hen the netork is not dense enogh, the connectiit reqirement in Theorem 1 is not satisfied, and therefore, cannot garantee the coerage. This problem can be soled ith dal neighbor set enhancement introdced in sbsection III-D. Figre 12 (b) shos the delier ratio of the enhanced scheme, here all neighbors ithin the normal transmission range r 2 are pt into the coered neighbor set, and onl neighbors ithin the redced transmission range r 1 are pt into the adertised neighbor set. With this enhancement, high delier ratio ( 90%) can still be achieed nder the highest mobilit leel. Oerall, Simlation reslts sho that balance beteen de-

11 lier ratio and broadcast redndanc can be achieed b adjsting the bffer zone idth based on the netork mobilit leel. As predicted b or probabilistic analsis, for each mobilit leel, high delier ratio can be achieed ith a bffer zone mch thinner than reqired b Theorem 2. The dal neighbor set enhancement is proed sccessfl in relaing the connectiit reqirement in Theorem 1, and achiees high delier ratio in sparse netorks. V. CONCLUSIONS In this paper, e hae proposed a mobilit management method based on the se of to transmission ranges. Using this mechanism, e hae also etended W and Dai s coerage condition to a dnamic enironment here netork topolog is alloed to change, een dring the broadcast process. In addition, connectiit, link aailabilit, and consistenc isses related to neighborhood information of different nodes hae also been addressed. The proposed scheme can also be etended to proide mobilit management for other actiities sch as topolog control in MANETs [26]. The constraint sed on r 2 r 1 in this paper is conseratie. Or probabilistic analsis sggests that high delier ratio can still be achieed ith a larger r 1. Simlation reslts sho that the proposed method and to enhancements achiee good balance beteen delier ratio and broadcast redndanc b adjsting the ale of r 1 based on the netork mobilit leel. In W and Dai s coerage condition, node id is sed to break a tie. We cold also se the notion of relatie mobilit [27], defined as absolte relatie speed aeraged oer time, for tie breaking. In general, a node ith high relatie mobilit is more prone to nstable behaior than a node ith less relatie mobilit and therefore shold be prned (from being a forard node) hen possible. In this case, relatie mobilit is calclated locall throgh some form of approimation and distribted throgh piggbacking ith reglar Hello messages. REFERENCES [1] Y.-C. Tseng, S.-Y. Ni, and E.-Y. 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Dai, Mobilit-sensitie topolog control in mobile ad hoc netorks, Oct. 2003, sbmitted for pblication. [27] B. An and S. Papaassilio, A mobilit-based clstering approach to spport mobilit management and mlticast roting in mobile ad-hoc ireless netorks, International Jornal of Netork Management, ol. 11, no. 6, pp , No.-Dec APPENDIX: SPECIAL CASES OF THE COVERAGE CONDITION W and Li s algorithm (static): W and Li [18] proposed a marking process to determine a set of gateas (i.e., forard nodes) that form a CDS: a node is marked as a gatea if it has to neighbors that are not directl connected. To prning rles are sed to redce the size of the resltant CDS. According to prning Rle 1, a gatea can become a nongatea if all of its neighbors are also neighbors of another node that has higher priorit ale; that is, s neighbor set is coered b. According to prning Rle 2, a marked node can be nmarked if all of its neighbor set is coered b to other nodes that are directl connected and hae higher priorit ales.

12 (a) Marking process (b) Rle 1 (c) Rle 2 (d) Rle k (e) Span (f) LENWB (g) SBA (h) Coerage condition Fig. 13. Node in the center of each sbgraph can be self-prned b the corresponding protocol. Nodes in the transmission range of node (the dashed circle) are neighbors of. Gra nodes hae higher priorities (e.g., higher id s) than. Black nodes are isited nodes that hae forarded the broadcast packet. Dai and W s algorithm (static): Dai and W [19] etended the preios algorithm b sing a more general prning rle called Rle k: a gatea becomes a non-gatea if all of its neighbors are also neighbors of an one of k other nodes that are connected and hae higher priorit ales. Rles 1 and 2 are special cases of Rle k here k is restricted to 1 and 2, respectiel. Span (static): Chen, Jamieson, Balakrishman, and Morris [20] proposed the Span protocol to constrct a set of forard nodes (called coordinators). A node becomes a coordinator if it has to neighbors that are not directl connected, indirectl connected ia one intermediate coordinator, or indirectl connected ia to intermediate coordinators. Before a node changes its stats from non-coordinator to coordinator, it aits for a backoff dela hich is compted from its energ leel, node degree, and the nmber of pairs of its neighbors that are not directl connected. The backoff dela can be ieed as a priorit ale, sch that nodes ith shorter backoff dela hae a higher chance of becoming coordinators. LENWB (dnamic): Scec and Marsic [21] proposed the Lighteight and Efficient Netork-Wide Broadcast (LENWB) protocol, hich comptes the forard node stats on-the-fl. Wheneer node receies a broadcast packet from a neighbor, it comptes the set C of nodes that are connected to ia nodes that hae higher priorit ales than. If s neighbor set, N() (i.e., N 1 ()) is contained in C, node is a nonforard node; otherise, it is a forard node. SBA (dnamic): Peng and L [16] proposed the Scalable Broadcast Algorithm (SBA) to redce the nmber of forard nodes. As in LENWB, the stats of a forard node is compted on-the-fl. When a node receies a broadcast packet, instead of forarding it immediatel, ill ait for a backoff dela. For each neighbor that has forarded the broadcast packet, node remoes N() from N(). IfN() does not become empt after the backoff dela, node becomes a forard node; otherise, node is a non-forard node. Stojmenoic s algorithm (hbrid): Stojmenoic, Seddigh, and Zinic [17] etended W and Li s algorithm in to as: (1) Sppose eer node knos its accrate geographic position, onl 1-hop information is needed to implement the marking process and Rles 1 and 2. That is, each node onl maintains a list of its neighbors and their geographic positions (connections among neighbors can be deried). (2) The nmber of forard nodes are frther redced b a neighbor elimination algorithm similar to the one sed in SBA. The difference among aboe special cases is illstrated b Figre 13. To hae a fair comparison, each node is eqipped ith onl 2-hop information. Node in sbgraphs (a), (b), and (c) can be prned b W and Li s algorithm. Node in sbgraphs (a) to (d) can be prned b Dai and W s algorithm. Node in sbgraphs (a), (b), (c), and (e) can be prned b Span. Node in sbgraphs (a) to (f) can be prned b LENWB. Node in sbgraphs (a) and (g) can be prned b SBA. Node in sbgraphs (a), (b), (c), and (g) can be prned b Stojmenoic s algorithm. Node in all sbgraphs can be prned b the coerage condition. A static protocol has onl gra nodes, hereas a dnamic protocol has both gra and black nodes.