Self-Organizing Hierarchical Routing for Scalable Ad Hoc Networking

Transcription

1 1 Self-Orgnizing Hierrchicl Routing for Sclble Ad Hoc Networking Shu Du Ahmed Khn Sntshil PlChudhuri Ansley Post Amit Kumr Sh Peter Druschel Dvid B. Johnson Rudolf Riedi Rice University Abstrct As devices with wireless networking become more pervsive, mobile d hoc networks re becoming incresingly importnt, motivting the development of highly sclble d hoc networking techniques. In this pper, we present the design nd evlution of novel protocol for sclble routing in d hoc networks s prt of the Sfri project. We develop probbilistic, self-orgnizing network hierrchy formtion protocol tht recursively forms the nodes of the d hoc network into n dptive, proximity-bsed hierrchy of cells. We develop hybrid routing protocol tht uses this hierrchy nd lso develop n ondemnd rective routing protocol to scle to lrge numbers of nodes. The mpping of unique node identifiers to hierrchicl ddresses is done using distributed hsh tble tht leverges the hierrchicl network structure. We evlute this sclble routing protocol through nlysis nd simultions, showing individully s well s together the performnce of the hierrchy formtion protocol, the overhed of ddress mpping, nd the performnce of the routing protocol. As devices with wireless networking become more pervsive, mobile d hoc networks re becoming incresingly importnt, motivting the development of highly sclble d hoc networking techniques. In this pper, we present the design nd evlution of novel protocol for sclble routing in d hoc networks s prt of the Sfri project. We develop probbilistic, self-orgnizing network hierrchy formtion protocol tht recursively forms the nodes of the d hoc network into n dptive, proximity-bsed hierrchy of cells. We develop hybrid routing protocol tht uses this hierrchy nd lso develop n on-demnd rective routing protocol to scle to lrge numbers of nodes. The mpping of unique node identifiers to hierrchicl ddresses is done using distributed hsh tble tht leverges the hierrchicl network structure. We evlute this sclble routing protocol through nlysis nd simultions, showing individully s well s together the performnce of the hierrchy formtion protocol, the overhed of ddress mpping, nd the performnce of the routing protocol. I. INTRODUCTION Ad hoc networking is n ttrctive technology for providing wireless internet ccess nd other wireless communictions services for mobile users, but current d hoc network routing protocols re limited in sclbility. In n d hoc network, individul mobile nodes cooperte to form network without the id of ny existing communictions infrstructure such s bse sttions or ccess points. Insted, ech mobile node cts not only s host but lso s router, forwrding pckets for other mobile nodes to llow nodes beyond direct wireless trnsmission rnge of ech other to communicte. With the rpid prolifertion of wireless devices, the use of d hoc networking is likely to grow, nd with it, the size of d hoc networks tht my be creted. At the sme time, the field of peer-to-peer, or decentrlized, self-orgnizing distributed systems hs seen significnt interest nd dvnces in recent yers nd hs opened new lterntives in providing services in lrge-scle networked systems. Work on these two res hs proceeded lrgely independently. The Sfri project is developing protocols nd lgorithms for providing lrge-scle mobile wireless network connectivity nd bsic network services, exploiting tight integrtion between d hoc networking nd peer-to-peer networking. In this pper, we present the design nd evlution of new self-orgnizing hierrchicl routing protocol for sclble d hoc networking, s prt of the Sfri project. The routing protocol is bsed on probbilistic, self-orgnizing network hierrchy formtion protocol tht recursively forms the nodes of the d hoc network into n dptive, proximitybsed hierrchy of cells. Routing of pckets is guided by this hierrchy nd by on-demnd rective routing, forming hybrid routing protocol cpble of scling to lrge numbers of nodes. The mpping of unique node identifiers to hierrchicl ddresses is done using distributed hsh tble tht leverge the hierrchicl network structure. We evlute our routing protocol through both nlysis nd simultions, showing the performnce of the hierrchy formtion protocol, the overhed of ddress mpping, nd the performnce of the routing protocol. Our evlution ddresses incresing size of the network in number of nodes, incresing mobility in the frction of nodes tht re mobile vs. sttionry, nd incresing trffic lod in number of dt pcket flows. Our nlysis is well mtched by our simultions, nd our results demonstrte the protocol s sclbility. In Section II of this pper, we describe the detils of the Sfri protocol rchitecture, including its self-orgniztion, routing, nd ddress resolution components. In Section III we present our modeling nd nlysis of Sfri, nd present our detiled, simultion bsed, performnce evlution in Section IV. In Section V, we discuss relted work in the re of sclble d hoc networking, nd conclude in Section VI. II. SAFARI ARCHITECTURE In this section, we provide high-level overview of the bsic Sfri rchitecture, nd then present the vrious components of Sfri routing in more detil. A. Overview Sfri is hybrid, hierrchicl routing protocol, using both proctive nd rective routing components. The hierrchy is formed s recursive orgniztion of nodes into cells, cells into supercells, nd so on, bsed on n utomtic self-selection of subset of the nodes to operte s drums. In generl, level k cells re grouped into level k + 1 cells, nd for simplicity, we refer to individul nodes s level 0 cells. We cll level 1 cells

2 2 lso fundmentl cells, s t this level, the cell is composed only of individul nodes. The drums re orgnized hierrchiclly, s well, with subset of the individul nodes self-selecting to become level 1 drums, nd itertively level k drums self-selecting to become level k + 1drums.Alevelk drum is t the sme time lso level i drum for ll i k. Ech drum hs unique identifier, nd ech drum t level i identifies cell t level i. The drum selection is bsed on distributed lgorithm thus requiring no centrlized coordintion. Nodes of the sme level re roughly eqully spced (in terms of hop counts) throughout the totl d hoc network. The drum identifiers crete hierrchicl ddress for ech node. Ech drum dissemintes loclity, hierrchy, nd routing informtion by trnsmitting periodic becon pckets, which re forwrded by ll nodes within well-defined scope in the network. A becon hop count nd n identifier for the originting drum provides nodes with sense for their loction within the network, which they store in the network using distributed hsh tble (DHT); crefully choosing multiple storge nodes improves robustness nd efficiency of lookup. The drums do not hve ny specil role in dt pcket forwrding; they simply provide sense of loction nd direction tht is used in routing. For sending dt pcket, the pcket is routed ccording to the hierrchicl ddress (or coordintes) of the pcket s source nd destintion, recursively routing towrds the drum for the destintion node s cell t ech level. To route towrds drum, Sfri normlly follows the reverse pth of the most recent becon from tht drum. Once the dt pcket is received by ny node within the destintion s fundmentl cell, tht node initites n on demnd route discovery for the trget node (if it does not lredy hve previous cched route) to complete the route. This ensures tht dt pckets do not hve to go through drums. This ensures tht drums re no more loded with dt pckets thn norml nodes. Locl route repir llows Sfri to overcome route filures in n on-demnd mnner nd reduces the need for more frequent becons; routing stte for drum is followed by dt pckets until new stte is recreted by lter becon. We now provide more detiled description of the components of the Sfri rchitecture The Sfri rchitecture owes its sclbility to the following fetures of the rchitecture: Trnsprency: Becons mintin hierrchy, keep loclity informtion up to dte, nd provide crucil routing informtion mtched to the loclity informtion. Hybrid routing: Proctive, hierrchicl routing for routing towrds the fundmentl cell of the destintion, where route discovery is costly, combines idelly with ondemnd routing for the lst mile, i.e., the fundmentl cell where owing to node mobility, proctive mintennce of precise loction becomes costly. Distributed solutions: Shred responsibilities, distribution of loclity informtion, nd self-selection reduce stress on individul nodes nd void overhed from voting, electing, nd coordinting. We now provide the design detils left unspecified so fr nd in prticulr, we ddress the issues of efficiency nd Fig. 1. Beconing scope A X Level i cell B Level i+1 cell sclbility. The three protocols tht provide the bsics for the Sfri rchitecture re s follows: self orgniztion, sclble routing, nddistributed ddress resolution. Further elements of the Sfri rchitecture which provide higher level services re beyond the scope of this pper. B. Self orgniztion In this section, we describe the lgorithms tht chieve nd mintin the desired hierrchicl orgniztion of the network, even under node mobility, node filures, nd prtition nd merging of networks. There re three bsic mechnisms which llow the Sfri rchitecture to self orgnize. 1) Beconing protocol: Ech drum periodiclly brodcsts n dvertisement of its existence long with some useful informtion. Such control pcket from drum of level n is clled level n becon. Ech becon contins the following informtion: 1) becon sequence number, 2) becon level nd coordinte which equl those of the emitting drum, 3) nd hop count which is set to zero t the emitting drum nd incremented by ech forwrding node. Adrumtleveln trnsmits becon of level n every T n seconds. These becons re forwrded by ll nodes within D n number of hops from tht drum. This forwrding rule llows becons to rech ll nodes tht could potentilly ssocite with the originting drum ccording to the Membership lgorithm described in Section II-B.3. For exmple in Figure 1, the dotted circle denotes ll nodes within D i hops of X, leveli drum. Higher level becons re emitted t lower frequency thn lower level becons. This is becuse mobile nodes cross over the regions covered by lower level drums more frequently thn they cross over the regions covered by higher level drums. For sclbility, T n nd D n re given by the geometric progressions: D n = α D n 1 = α n 1 D 1 ; T n = β T n 1 = β n 1 T 1 (1) where α > 1ndβ > 1 re system prmeters. D 1 is bsed on the optiml hop count tht the on demnd routing protocol, used t the level of the fundmentl cell, cn hndle efficiently. To increse the efficiency of sclble routing (Section II-C), becon of level n is lso forwrded by ll nodes in the level n + 1 cell of the originting drum. The exct mechnism by which cell structure is formed is discussed in Section II-B.3. For node X in Figure 1, the becons re forwrded throughout the level i + 1 cell of which X is member. The forwrding

3 3 of becons is hence union of the two forwrding rules mentioned bove. All nodes store the becons they forwrd in cche of becons, clled the Drum Ad Hoc Routing tble (DART). This cche is used for self-orgniztion s well s routing. In ddition to mintining ll the vribles contined in becon, node lso stores in its DART the time of reception of the becon nd the node identifier from which it received the becon in the DART. The ltter will llow following of the reverse pth of the becon, while the former llows to keep the cche up to dte. Upon receipt of becon, new DART entry is formed nd timer for tht entry is strted. Whenever new entry is inserted into the DART or DART entry expires, the drum level selection nd the Membership lgorithms re invoked. As mentioned erlier, the only specil function of drum is to originte becons. A drum hs no specil or ctive role in routing or in the overly mintennce. In prticulr, dt pckets re only routed towrds but not through drums, s will be described in Section II-C. Thus, ll nodes shre the becon trnsmission worklod (origintion or forwrding) eqully. 2) Drum level selection lgorithm: In order to be efficient under dynmic chnges of the network such s mobility nd node filures, new drums cn form nd existing drums cn retire. This lgorithm runs fter ech chnge in the DART nd ssures tht eventully the DART stisfies the following conditions. For node of level n: 1) the DART contins t lest one non-expired becon of leveln + 1drumtmostD n+1 hops wy, 2) there is no non-expired becon of level n drum less thn h D n hops wy (0 < h < 1 is hysteresis fctor), 3) there re t lest two non-expired becons of t lest level n 1. The wy by which the desired stte of the DART is chieved is by chnging the node s level ppropritely such tht the invrints re met. If condition 1 is violted, the level of the node is chnged to n + 1 nd the node wits rndom bck-off time until it nnounces its new level with its level n + 1 becon. This does not pply to the highest level drum; otherwise, the highest level drum would increse its level indefinitely. A drum infers tht it is the highest level drum if its DART does not hve non-expired becons from drum of its level. If condition 2 is violted, it mens tht two or more drums of the sme level re too close to ech other. The drum with the highest node identifier remins t the sme level, nd the rest of the drums reduce their level by 1. The fctor h cretes hysteresis which prevents oscilltions in the drum retirement process. By oscilltion, we men n unstble sitution of retirements of drums nd formtion of new drums to compenste for the retirement, leding to new retirements, nd this process continuing unendingly. Indeed, level n drum retiring could cuse condition 1 to be violted for other nerby nodes which then will increse its level. However, these nodes will be t lest D n hops wy from ny level n drum. Since conflict between drums requires this distnce to reduce to h D n < D n there is no oscilltion. For the rest of the pper, we chose h = 1/2. Condition 3 is for efficiency nd ensures tht ny drum in the Sfri tree hs more thn one brnch hnging off it. 3) Membership lgorithm: The presence of drums induces nturl clustering of nodes. Ech node ssocites with drum of level one greter thn its own level, nd selects this drum ccording to the contents of its DART. Typiclly, node ssocites with the one higher level drum tht is the lest number of hops wy. A node s ssocition is mde individully nd is not communicted bck to the drum. A node invokes the membership lgorithm fter it hs run the drum level selection lgorithm. In its bsic version, for node of level n, this lgorithm chooses the closest of ll drums of level n + 1 for which this node hs DART entry tht hs not expired. However, this might led to nodes ner the cell border to oscillte between drums. In order to prevent such oscilltions this rule to chnge the ssocited drum is enhnced by ssigning ech DART entry weight clculted from the frequency, the distnce, nd the number of becons received. The node ssocites with the drum corresponding to the DART entry with the highest weight. In our design presented in this pper, we enforce tht the new drum is t lest 2 hops closer thn the current one, nd tht t lest 3 becons hve been received from the new drum. The membership lgorithm cnnot ensure tht the node ssocites with drum tht is t most D n hops wy. This is the duty of the drum level selection lgorithm. Coordinte selection: The membership lgorithm gives unique ncestry for ech node. Using this membership informtion, ech node is ssigned coordinte bsed on the drum structure. This coordinte plys vitl role in routing. The Sfri hierrchicl tree structure fosters simple scheme to provide coordintes by trnsferring the loclity informtion encoded in the tree. Every node in the network is ssigned coordinte. The coordinte of drum t level i is the conctention of the coordinteof the level i+ 1 drum with which it ssocites nd rndomly generted unique number. Thus, if COORD(D i ) denotes the coordinte of level i drum, D i nd PARENT(D i ) denotes the level i+1 drum with which node (not necessrily drum) ssocites, then we hve the following COORD(D i )=COORD(PARENT(D i )).RAND(b) where RAND(b) denotes uniform rndom number of b bits. With lrge vlue of b the probbility tht two drums t the sme level will chose the sme rndom number cn be mde negligible. The coordinte of lef node L, isgivenby COORD(L)=COORD(PARENT(L)) When node powers on, it ssocites with drum t level 1 nd sets its coordinte to the coordinte of the drum with which it ssocites. This implies tht ll nodes in fundmentl cell hve the sme coordinte. Suppose drum D i t level i hs the coordinte [D k D k 1 D i D i 1 D 1 ] nd decides to decrese its level from being drum t level i to drum t level i 1. Suppose fter doing so it ssocites with nother drum t level i, B i, which hs the coordinte [B k B k 1 B i B i 1 B 1 ]. Then the drum tht decresed its level will be drum t level i 1 nd

4 4 its coordinte will be [B k B k 1 B i D i 1 D 1 ]. On the other hnd if drum D i t level i hs the coordinte [D k D k 1 D i+1 D i D 1 ] nd decides to increse its level to drum t level i + 1 then it chooses uniform rndom number D i+1 nd sets its coordinte to be [D kd k 1 D i+1 D i D 1 ]. However, before chnging its coordintes, the drum listens for becons from other drums t level i + 1 in order to check for collisions. If there is collision then the node picks nother uniform rndom number insted of D i+1 nd uses tht insted. The level n becon scope is extended beyond the TTL D n to the cell of level n + 1 in order to improve on the efficiency of routing nd self-orgniztion. To this end, becon of level n is forwrded by node unless the n + 1 coordinte of the node nd the becon re different. This limits the scope of the becon flood. 4) Discussion: The beconing protocol requires notion of cells nd coordintes to determine the becon scope; the membership lgorithm in turn relies on becons to compute the hierrchy nd coordinte. To clrify the sitution let us mention tht the becon scope is t lest certin number of hops, the becon TTL. This will ssure proper functioning of the lgorithms even with temporrily dysfunctionl cell structure. The becon scope is widened to the next upper cell for efficiency in routing nd not for correctness of the protocol. At strt up, nodes hve n empty coordinte nd will forwrd every becon. If no becon is received for timeout period, node will increse its level to become drum. The becons of the first few drums will rech throughout the network. Once t lest two of them hve incresed their levels to become level 2 drum will the level 1 becon scope be confined by the cell structure. When two Sfri d hoc networks merge, i.e., when nodes of two Sfri networks with tree depth n nd m n overher ech other s becons then these becons re not stopped immeditely nd penetrte the other network. The level k becons with k m, in prticulr, re forwrded throughout both Sfri networks for the simple reson tht either the becon or the forwrding node hs only m coordintes nd thus cnnot differ in the k+1 coordinte. The smller network quickly lerns of the high level drum in the other network, nd ssocites with it, updting its coordintes in the process. This corresponds to merging smller tree t the pproprite level into the lrger tree. If the depths hppen to be equl, one will increse its level to become the new root, s discussed previously. C. Sclble routing protocol Routing in the Sfri hierrchicl rchitecture cn be divided into two phses. Given the hierrchicl ddress of the destintion node, the first phse, clled inter-cell routing, isto deliver the pcket to the fundmentl cell where the destintion node lies in. Once the pcket reches the fundmentl cell of the destintion, the second phse, clled intr-cell routing, will deliver the pcket to the destintion node within tht fundmentl cell. Inter-cell routing is bsed on the destintion s hierrchicl ddress nd the becon records stored in the DART of the intermedite forwrding nodes. We ssume the existence of bidirectionl wireless links, which is true for the commonly used protocol in the MAC lyer. With this ssumption, the inter-cell routing cn be supported by following the reverse pths of the becons emitted by the drums of the cells where the destintion node belongs to. For intr-cell routing, ny stte of the rt on-demnd routing protocols cn be used, since the size of the fundmentl cell is within their cpbility. We choose DSR s the intr-cell routing protocol for its proved stbility with high performnce in smll scle d hoc networks [1]. When source node S with coordinte [S n S n 1 S 1 ], hs pcket to send to node D, S retrieves the coordinte [D n D n 1 D 1 ] of D using the DHT ddress lookup service described in Section II-D, We clim tht there must exist n integer k,1 k n, such tht S i = D i for ll k i n, wheren is the number of levels in the hierrchy. If k = 1, then S nd D belong to the sme fundmentl cell nd intr-cell routing is invoked. Otherwise, inter-cell routing is invoked. If inter-cell routing is pplied, the source S will ttch the coordinte of D into the pcket heder before sending it out so tht the following downstrem nodes cn get the coordinte of the destintion from the pcket insted of hving to do seprte DHT lookup. When node hs pcket to forwrd, it will use the sme logic s the source to see whether to keep on doing the inter-cell routing or to pply intr-cell routing. Let s look t n exmple. In Figure 2, it shows how pcket is sent from the source node S to the destintion node D. S uses inter-cell routing first, long the route lbeled by nd b, to rech the fundmentl cell of destintion node D. Within the fundmentl cell, intr-cell routing is used to deliver the pcket to the destintion, long the route lbeled by c. The route mrked with is the reverse pth of the becon emitted by the level 2 drum A, whichd belongs to, while the route mrked with b is the reverse pth of the becon emitted by the level 1 drum B, which D is directly ssocite with Fig. 2. S b b Sfri routing overview 1) Proctive strtegy in inter-cell routing: The bsic strtegy of the inter-cell routing is to tke the reverse pth of the becons tht were herd previously. When becon is received, the node stores the immedite upstrem node s b b b A b c D c B

5 5 identifier in its DART (long with the informtion contined in the becon). When the node hs dt pcket to send to the specific cell, it cn uses this stored informtion to get the next hop towrd tht cell. As illustrted in Figure 1, ech drum emits its becon to ll the nodes in its own cell s well s the nodes in the cells of its siblings (the sme level drums which lso shre the sme higher level drum). This mechnism gurntees tht ny node tht is in the sme super-cell will hve the routing informtion to ll the fundmentl cells in this super-cell in the sense tht it cn reverse the becon pth. Unlike some clustered routing protocols in d hoc network, which ssumes the existence of super powered cluster heds, drums in the sfri hierrchicl structure need not be prt of the route tken for dt trnsmission. As we cn see in Figure 2, once the pcket enters the level 2 cell of A, ny node in tht cell will hve the routing informtion to the fundmentl cell B nd the pcket will not go through the drum A. For inter-cell routing, ech pcket contins the following informtion in its heder, till the pcket reches the fundmentl cell of the destintion: Length:Theprefix mtch length between the destintion s coordinte nd the entry in the DART tht ws used to forwrd this pcket. We define the prefix mtch length between two coordintes [B n B n 1 B 1 ] nd [C n C n 1 C 1 ] s the lrgest integer k such tht B i = C i ; n i < n k. Sequence number: The sequence number of the becon corresponding to the entry in the DART tht ws used for forwrding this pcket. In order to forwrd dt pcket for destintion, node does the following: 1) The node serches its DART to find out the entry with the mximum prefix mtch length with the destintion s coordinte 2) If the entry with the mximum prefix mtch length hs prefix mtch length > Length contined in the pcket, then the node updtes the vlues of Length nd Sequence number ccording to the entry in the DART. The pcket is then forwrded to the hop from which the becon corresponding to the entry in the DART ws received. 3) If the mximum prefix mtch length is equl to the Length contined in the pcket, then if ny such entry hs corresponding becon sequence number which is no less thn the Sequence number crried in the pcket, then use tht DART entry to forwrd the pcket fter updting the Sequence number in the pcket. 4) If the mximum prefix mtch length (over ll entries in the DART) is less thn the Length contined in the pcket, then the node invokes locl route repir s described below. Inter-cell routing is loop free, becuse for ny given time, every node will hve only one unique pth to the destintion. The DART entries give the reverse pths of the becons, which re lwys trees nd hence loop-free. The pths trversed by pckets cn be considered s being composed of brnch segments from different trees. When pcket is delivered towrds drum, the pcket lwys trvels upwrd towrds the root long the brnches of the corresponding tree, which is obviously loop free. And once the pcket jumps to nother tree, it mens tht the prefix mtch length increses, the pcket will never jump bck to the previous trees since the forwrding lgorithm requires tht the node trversl cn only be from shorter prefix length to longer prefix length. Therefore, the entire trversed pth is loop free. 2) Rective strtegy in inter-cell routing: The inter-cell routing scheme s described bove requires the node forwrding the pcket to follow the reverse pth of the drum becons. But this might not be possible in the following circumstnces: When node received pcket which follows the reverse pth of some specific drum s becon, the corresponding becon entry t the node my hve lredy expired. Also, due to prtitions in the network or due to the unrelible wireless medi, some becons might not rech their intended scope. As result of these, node ttempting to forwrd pcket might not hve ny useful informtion in its DART. When forwrding node tries to send the pcket to the next hop, the trnsmission could fil due to the mobility of nodes or the flky conditions of the wireless medium,. This filure cn be notified by its own MAC lyer if the MAC protocols uses request nd cknowledge mechnism, similr to the MAC protocol. Compred with the previous cse, this sitution is much more frequent in wireless networks nd cn potentilly degrde routing performnce substntilly. If such situtions rise, triggered by filed serch in the BART or by n unsuccessful trnsmission, Locl Route Repir is invoked in the forwrding node. Locl route repir is used to find n lternte route to keep on forwrding the pckets. The node sends out ROUTE REQUEST pcket to its round neighborhood within hop-limited rnge fter the node buffers the pckets which could not be delivered. The ROUTE REQUEST pcket contins the following dditionl informtion: 1) the current mximum prefix length mtch in the node s DART 2) the sequence number for the becon being followed 3) the coordinte of the unrechble finl destintion A node receiving the ROUTE REQUEST serches its DART for the coordinte of the destintion. If the node finds longer prefix mtch for the destintion coordinte or if the node finds sme length prefix mtch but with higher sequence number, the node sends ROUTE REPLY contining the mtching DART entry, bck to the origintor of the ROUTE REQUEST. If node receiving ROUTE REQUEST cnnot reply to the request nd if the request is not duplicte of n erlier received request, the node rebrodcsts the ROUTE REQUEST. Once the ROUTE REPLY goes bck to the requester, the previously buffered pckets will be redirect through the pth the ROUTE REPLY just trversed. A node receiving multiple ROUTE REPLY pckets chooses the ROUTE REPLY with the longest prefix mtch. If two replies hve the sme length prefix mtch, the node ccepts the reply from the closer responder.

6 6 3) Rective intr-cell routing: When n intermedite node receives pcket, it checks if itself is in the sme fundmentl cell s the destintion, i.e. its coordinte mtches with the coordinte of the destintion. If the coordintes mtch, then the pcket hs reched the fundmentl cell of the destintion nd intr-cell routing is used to send the pcket to the destintion. While ny d hoc network routing protocol cn be used within the fundmentl cell, we choose to use DSR [2] s it is fully rective protocol which hs been shown to perform well [1]. DSR is source routing protocol, i.e. ech pcket sent using DSR contins source route. The DSR protocol consists of two mechnisms: Route Discovery nd Route Mintennce. To perform Route Discovery for destintion node D, source node S brodcsts ROUTE REQUEST tht gets flooded through the network in controlled mnner. This request is nswered by ROUTE REPLY from either D or some other node tht knows route to D. To reduce frequency nd propgtion of ROUTE REQUESTs ech node ggressively cches source routes tht the node lerns or overhers. Route Mintennce detects when some link over which dt pcket is being trnsmitted breks. When such route brekge is detected, ROUTE ERROR is sent to S. Upon receiving ROUTE ERROR, S cn use ny other route to D tht it hs in its route cche, or S cn initite new Route Discovery for D. In trditionl DSR, ROUTE REQUEST my be flooded throughout the entire network, thus mking Route Discovery incresingly expensive with the increse in network size. Since in our cse of intr-cell routing, it is lredy known tht the destintion exists in the sme fundmentl cell, the Route Discovery is limited to the dimeter of the fundmentl cell. As different fundmentl cells my hve different sizes, the Route Discovery rnge is bsed on the dynmic membership of the nodes, insted of predefined hop count. Specificlly, whenever node received Route Discovery messge, it compres it s own coordinte with the inititor s coordinte. The node then forwrds the pcket only if the two coordintes mtch. This technique is sclble, s the fundmentl cell size does not increse with the network size. The origintor A my hve the wrong coordinte of the destintion B, s B might hve chnged it s membership recently. To tke dvntge of the high probbility of the destintion still remining in the vicinity of it s previous fundmentl cell, hop count threshold is introduced in the Route Discovery phse which llow the ROUTE REQUEST pckets to go few hops beyond the fundmentl cell. In this modified Route Discovery, ech node forwrding ROUTE REQUEST checks if its own coordinte is different from tht of the origintor of the ROUTE REQUEST nd if so, increments the hop count field in the pcket. If the hop count is lower thn threshold, then the request is forwrded, else it is dropped. This cretes fuzzy boundry of cell llowing routing with lesser overhed. D. Address resolution The routing protocol described in Section II-C delivers pckets to the intended destintion given tht destintion s current coordinte, which depends on its current loction in the network. However, typiclly senders wish to ddress pckets using the destintion s permnent identifier. To enble this, distributed ddress resolution service mps node s identifier to its current coordinte. Clerly, n pproprite service must be sclble, efficient, nd tolernt of node filures nd mobility. In ddition, to stisfying the needs of d hoc wireless environments, it must observe loclity, such tht lookup of nerby node does not require communiction with distnt node. The service is implemented in mnner tht is similr to distributed hsh tble (DHT) but is dpted to the needs of mobile d hoc environment. A conventionl distributed hsh tble stores key,vlue pirs by hshing the key nd storing the ssocited tuple t set of overly nodes whose unique identifiers re closest to the resulting hsh vlue. However, unlike n overly-bsed DHT, our service directly exploits the hierrchicl structure provided by the buoy protocol. Therefore it does not incur dditionl mintennce overhed. Also, the spce of node coordintes, s opposed to the spce of node identifiers s in overly-bsed DHTs, is interpreted s the DHT s identifier spce. Finlly, our service inserts replics of ech tuple in loclity-wre fshion, to stisfy the needs of n d hoc network environment. Ech node inserts the tuple (IP ddress, coordinte) t set of k nodes throughout the network where k is the repliction fctor. The set k is determined by hshing the node s identifier k times, nd choosing the nodes whose present coordintes re closest to ech of the hsh vlues. The node reinserts the tuple whenever its coordinte chnges, or when given refresh intervl hs pssed. Any node cn lookup the coordinte of nother node by hshing the node s identifier nd sending query towrds one of the resulting coordintes. With pproprite choices for k nd the refresh intervl, this scheme provides relible ddress resolution despite the movement nd filure of nodes. This bsic scheme is similr to the one used in lndmrk routing [3]. Unfortuntely, the bsic scheme does not stisfy the loclity requirements of n d hoc network, since looking up node requires communiction with node tht my be distnt in the network. Similrly, updting node s coordinte requires communiction with k nodes with rbitrry loctions in the entire network. To preserve loclity, we ugment the bsic scheme s follows. In ddition to inserting tuples t the k rndom coordintes, we insert the tuple lso t k nodes closest to the node s present coordinte, with the i lest significnt coordinte components replced by the rndom hsh vlue, for i rnging from 1 to the number of levels in the buoy cell hierrchy minus 1. Thus, we store tuples t nodes tht re incresingly closer to the node s present position in the network. Moreover, when node A s coordinte chnges only in the i lest significnt components, it needs to reinsert its tuple only t nodes whose distnce is proportionl to i, thus reducing the cost of mobility. Thus, remote communiction is only required when node moves cross high-level cell boundry. Coordintes stored t greter distnce my be inccurte in the lest significnt components s result of this technique,

7 7 but the correct coordinte cn be determined by itertively checking the closer tuples during lookup. When node A looks up node B s coordintes, it proceeds by itertively querying nodes t greter distnce from A, usingthe sme technique of coordinte prefix substitution. The mximl distnce tht query hs to trvel is now relted to the present distnce between node A nd node B in the network, thus reducing the cost of lookups. In ddition, ech node in the system cches the coordinte of node it hs recently looked up or otherwise lernt. This cching reduces the lod on the lookup service nd reduces the totl pcket trnsmission ltency in the common cse. We will present n experimentl evlution of the lookup service in Section IV-B. 1) Fult tolernce: It is likely tht one of the nodes storing coordinte fils or becomes unrechble. This is countercted by replicting the tuple t different hsh loctions s described erlier. The use of good hsh function distributes these replics widely through the network, thus reducing the likelihood of tuples becoming unvilble. In ddition, ech node tht stores tuple lso brodcsts tht tuple for its neighbors to store. This llows prticulr tuple to remin vilble even if the originl node storing it hs filed or deprted. Despite these mesures, it is possible node s coordinte becomes unvilble due to series of node filures or movements. To minimize the probbility of such loss, ech node periodiclly refreshes its coordinte. The refresh period should be more frequent for tuples stored close to the node nd less frequent for distnt tuples nd is chosen dynmiclly ccording to the observed chrcteristics nd stbility (node mobility nd churn) of the network. III. MODELS AND ANALYSIS This section proposes nd vlidtes the models tht we hve used to chrcterize the drum protocol nd the control overhed in the Sfri rchitecture. A. RSA model for drum formtion The Rndom Sequentil Adsorption (RSA) [4] model which is encountered in the description of moleculr dsorption processes lets us estimte the number of drums tht form, by the time the drum protocol hs converged. A one dimensionl version of the RSA model ws studied by Renyi [5] nd is populrly clled the cr prking problem. Consider street of length L. Crs of unit length rrive t rndom points in the street nd ttempt to prk t tht point. A cr prks if the lredy prked crs llow enough room t tht loction for it to prk. It leves otherwise. This process continues until no empty spot of t lest unit length remins. The prking process is sid to hve reched the jmming limit. The frction of street spce occupied by the crs is clled the pcking density. Renyi mthemticlly showed tht the verge pcking density t the jmming limit is 74.75% [5]. Only experimentl results re vilble for higher dimensionl cses (e.g. Hyperspheres prking in hypervolumes). The verge pcking density of the RSA process of circles prking on plne (2-D RSA) is 54.7% [6]. A limit theorem of Coffmn et l. [7] ensures tht the verge vlue of the pcking density converges when the prking hypervolume becomes lrge. In the following sections we consider d hoc networks of nodes in two dimensionl spce nd use the 2-D RSA model of discs. 1) The instntneous propgtion pproximtion: Consider two nodes A nd B, within D 1 hops of ech other, which just powered ON nd re witing to her from level 1 drums. The nodes wit for rndom time, uniformly distributed between [T min,t mx ], before turning into level 1 drums if necessry. Let T be the time for pcket to trverse D 1 hops. If T mx T min T then, with high probbility, one of the nodes will her becon from the other node before deciding to become drum nd so will not become drum. Therefore with high probbility, level 1 drums re seprted by t lest D 1 hops. The instntneous propgtion ssumption sttes tht level 1 drums re seprted by t lest D 1 hops, with high probbility. Extending the rgument to ll levels, level i drums re seprted by t lest D i hops, with high probbility. 2) Drum formtion conforms to the RSA model: Under the instntneous propgtion pproximtion, ll level 1 drums re t distnce of t lest D 1 hops. Thus, fictitious discs of rdii D 1 /2 hops centered t the drums do not overlp. This cn be thought of s nodes ttempting to prk. A node ttempts to prk disc of rdius D 1 /2 hops when its witing timer expires. A prking ttempt succeeds if the disc does not collide with n existing disc nd fils otherwise. A filure is equivlent to node finding level 1 drum within D 1 hops before its witing timer expires nd hence deciding not to become drum. The drum formtion process will proceed s long s disc cn prk without colliding nd when it completes no more discs cn be plced. This is becuse if it were indeed possible to plce disc t node without conflicts then tht node is t lest distnce of D 1 hops from every level 1 drum nd hence will hve tendency to become drum itself. If n is the verge number of level 1 drums tht form, then using the fct tht the prking density t the jmming limit is 54.7% we find n = N (2) π D2 1 4 ρ where N is the number of nodes in the network. ρ is the node density in the hop metric sense, its vlue depending on the trnsmission rnge of the rdio signl nd the sptil density of nodes. From simultions, we estimted vlue of ρ to be 1.4 for node density of 10 per rdio rnge nd rdio rnge of 250 meters. The bove eqution expresses tht the fictitious discs round the drums cover 54.7% of the nodes. The plot in Figure 3 ws obtined by simulting the drum protocol in ns-2 for 100 seconds with 500 nodes. The mobility model is modified billirds bll model with rndom reflection ngle upon hitting simultion surfce edges. Node speeds re uniformly distributed between 5 nd 15m/s. The plot shows the number of level 1 drums per node (n/n) t 100s, t which time the drum formtion process is complete. The witer timer expires uniformly in [0,150s]. Hence the instntneous pproximtion holds. The simultion shows tht the RSA model successfully predicts the number of drums tht form fter convergence of the drum protocol.

8 8 Fig. 3. Number of level 1 buoys per node Theoreticl Simultion D 1 Number of level 1 drums: ns-2 simultion For higher level drums the prking problem becomes constrined prking problem ( level 2 drum should lso be level 1 drum). The prking substrte (lower level drums) does not look like continuum to the higher level drum formtion process. The pproprite model is the RSA- RS (RSA-Rndom Sites) [8]. The model effectively reduces the pcking density little. From Eqution 2 the following eqution holds: n i = α i ( D i+1 ) 2 (3) n i+1 D i where n i is the number of level i drums nd α i is the rtio of the verge pcking densities of the RSA-RS process ssocited with level i drums nd the level i + 1drums.Since the pcking density decreses with the level slightly, α i is lrger thn but close to unity. B. Collision model for drum retirement When two level n drums drift to within h D n /2 hops of ech other, one of them will retire. We cn think of this s collision of two fictitious discs of rdii h D n /2 hops. We cn use results from sttisticl physics of moleculr collisions to compute the frequency of retirements [9]. Adpting the theory for two dimensionl discs we obtin the number of level n drum retirements per second in the network to be AD n v verge ρ 2 2 (4) where v verge is the verge velocity of the nodes, A is the re covered by the network nd ρ is the sptil density of level n drums. Using the RSA model results to substitute for ρ, the bove expression simplifies in functionl form to (N 2 /AD 3 n ) which is Θ(1/D 3 n) level n drum retirements per second per unit re (see Eqution 8). Thus the stbility of the drums increses with the level of the drums. Drum formtion rte t equilibrium is the sme s Eqution 4 if we ssume firly stble popultion of drums when equilibrium hs been reched. C. Overhed chrcteriztion This section chrcterizes some of the control overhed by using the models previously described. 1) Drum flooding overhed: Eqution 3 sys tht for every level i + 1 drum there re α i (D i+1 /D i ) 2 level i drums where α i is proportionlity fctor which is close to unity. Consider network with L levels (L is O(logN)) of drum hierrchy. Let the level i drum emit drum pckets once every T i seconds. A level i drum brodcst reches ll the nodes in the next higher level (level i + 1) cell. So node will receive drum pckets from ll level i drums which re within the sme level i + 1 cell which contins this node (α i (D i+1 /D i ) 2 of them) for i running from 1 to L 1 nd from the highest level drum. Therefore, overhed due to drum floods X drum,definedby the number of pcket forwrded per second per node is: X drum α 1 D 2 2 D T 1 +α 2 D 2 3 D α L 1 T 2 D 2 L D 2 L 1 1 T L T L (5) The ctul overhed due to drum floods is little greter thn tht shown in the bove eqution becuse becon floods propgte minimum number of hops (D i ). Therefore level i drum s pckets rech some nodes of neighboring level i+1 cell (like A in Figure 1) if the drum is t the border of the level i + 1 cell. But the error in Eqution 5 is negligible. This is becuse such overhering nodes live t the border of the cell nd hence re fr fewer thn interior nodes (like B in Figure 1) of cell. Moreover such node will her leked pcket only once for every, order of, (D i+1 /D i ) 2 brodcsts from its own level i + 1 cell. D i s nd T i s re geometriclly incresing s shown by Eqution 1. Hence, Eqution 5 implies tht X drum = Θ(1). 2) Frequency of cell chnges for node: A node s coordinte could chnge if the node moves into new cell. Since the verge interspcing (in hops) between two level i + 1drums is proportionl to D i+1, if the verge velocity of the level i drum node is v, it will cross the boundry of its level i+1 cell in time proportionl to D i+1 /v. In prticulr the frequency with which node moves over to n djcent fundmentl cell is proportionl to v/d 1. Totl number of coordinte chnges due to cell crossover Liner fit Simultion /D 1 1 Fig. 4. Level 1 cell crossing frequency follows D1 lw Figure 4 shows the result of n ns-2 simultion. The simultion is run for 100 seconds. The dt during the first 25 seconds ws discrded to remove initil trnsient behvior. The x-xis is the inverse of D 1 nd the y-xis is the totl number of coordinte chnges for ll 500 nodes due to level 1 cell crossings of the nodes. It is seen tht the number of

9 9 coordinte chnges due to level 1 cell crossings follows 1/D 1 lw. 3) DHT control overhed chrcteriztion: Nodes updte the DHT on-demnd when their coordintes chnge. Below we nlyze the overhed in the three circumstnces tht cn cuse node to chnge its coordinte: Cse 1: A level i drum crosses the boundry of its level i + 1 cell, in which cse the coordintes of ll the nodes which re ssocited with this drum chnge in the (i + 1)th digit from the lst. In prticulr, if non-drum node ( level 0 drum) moves into new fundmentl cell within the sme level 2 cell, its coordintes lst digit will chnge. As ws concluded in the previous section, node s coordintes ith digit from the lst, chnges with frequency of β(1/d i ) times per second for some constnt β which is independent of the D i s. If node s coordinte chnges beginning t the ith digit from the lst, it updtes its coordinte t ll its loctor nodes (nodes tht store its coordinte) which re in the sme level i+1 cell s this node is (loclity of updtes condition). Those re the m loctor nodes whose coordintes differ from this node s coordinte in the lst digit only, long with the m loctors whose coordintes differ from this node s coordinte in the lst two digits only nd so on until level i (for simplicity we ssume m = 1 in the reminder of this section). However, the verge hop distnce of loctor node whose coordinte is obtined by hshing nd replcing ll but the lst j digits with the coordinte digits of the node in question is proportionl to D j+1, becuse such node could be nywhere in the level j + 1 cell whose dimeter is of the order of D j+1 hops. Therefore bout D j+1 nodes re involved in forwrding the DHT updte to tht loctor node. Therefore the DHT updte overhed mesured in pckets/node/second generted due to nodes chnging their i th level drum is proportionl to (D D i+1 ) 1 = 1 i+1 D j (6) D i D i The totl overhed is obtined by summing up the bove for ll levels. Hence if we denote by X DHT 1 the overhed per node per second through DHT updtes triggered by mechnism I, then L 1 X DHT 1 = i=1 α i D i i+1 j=2 j=2 D j (7) where α i s re constnts independent of the D i s. If we choose D i s to be geometriclly incresing then the bove sum is 0(L) where L = 0(log(N)). Cse 2: If drum retires, then nodes in the vicinity will chnge their coordinte. Consider two drums of levels i nd j. Assume m = min(i, j). If these two drums come within D m /2 hops of ech other one of them will retire. This will led to some nodes chnging their coordintes nd updting them in the DHT. More specificlly the coordintes will chnge in their mth digit from the lst digit becuse level m drum hs retired. The number of such nodes chnging their coordintes is proportionl to the cell size of the level m cell which is in turn proportionl to D 2 m, s inferred from Eqution 2. These nodes will updte the DHT by updting their loctor nodes nd will therefore give rise to n updte overhed. The frequency with which retirement of level m drums hppens is described by the collision model. From Eqution 4, the totl number of collisions per unit re per second between level m drums is proportionl to D m ρ 2 m,whereρ m is the sptil density of level m drums. By collision, we men two drums drifting so close s to led to retirement of one of them. But ρ m = n m /A where A is the re of the network nd n m is the totl number of level m drums in the network. But from the RSA model described previously, n m is proportionl to N/D 2 m where N is the totl number of nodes in the network. Therefore, the totl number of collisions per second in the network between level m drums is proportionl to AD m ρ 2 m = AD n 2 m m A 2 D m N 2 A D 4 = N2 m AD 3 (8) m But ech collision is going to led to order of D 2 m nodes chnging their coordintes. But these coordinte chnges re occurring in the mth digit from the lst nd hence they incur forwrding overhed proportionl to (D D m+1 ). Therefore the per second node pcket product ssocited with the DHT updte overhed due to level m drum retirements is proportionl to N 2 AD 3 m D 2 m (D D m+1 ) (9) Hence the per node pcket overhed per second is 1/N th of the bove nd simplifies to N α m (D D m+1 ) (10) AD m where α m is constnt of proportionlity which is independent of the D i s. We sum up the bove expression over the drum levels to obtin the totl overhed. If we denote by X DHT 2 the overhed due to mechnism II in pckets per node per second, then X DHT 2 = L 1 m=1 α m ρ D L D m+1 = D m i=1 i+1 β i D i j=2 D j (11) where ρ is the sptil density of nodes mesured in nodes per squre meter nd α m s re proportionlity constnts independent of the D i s. It is remrkble tht X DHT 2 hs the sme form s X DHT 1 nd hence is 0(log(N)). Tht is, the overhed incurred by drum retirements nd cell crossovers re of the sme functionl form. Cse 3: If new drum forms, then nodes in the vicinity will chnge their coordinte. Under equilibrium conditions the drum popultion t ny level i fluctutes bout men vlue. Thus roughly speking for every level i drum retiring new level i drum ppers. Thus the retirement rte is equl to the formtion rte t equilibrium. But for every level i drum ppering the number of nodes tht will experience chnge in the coordinte in the ith digit is proportionl to D 2 i, the order of the size of level i cell. These nodes will updte the loctor nodes. Therefore by rguing exctly s we rgued for the previous cse, we rrive t the sme expression for the per node per second pcket overhed