A dynamic multicast tree based routing scheme without replication in delay tolerant networks

Transcription

1 Accepted Mnuscript A dynmic multicst tree bsed routing scheme without repliction in dely tolernt networks Yunsheng Wng, Jie Wu PII: S0-()00- DOI: 0.0/j.jpdc Reference: YJPDC To pper in: J. Prllel Distrib. Comput. Received dte: Februry 0 Revised dte: September 0 Accepted dte: November 0 Plese cite this rticle s: Y. Wng, J. Wu, A dynmic multicst tree bsed routing scheme without repliction in dely tolernt networks, J. Prllel Distrib. Comput. (0), doi:0.0/j.jpdc This is PDF file of n unedited mnuscript tht hs been ccepted for publiction. As service to our customers we re providing this erly version of the mnuscript. The mnuscript will undergo copyediting, typesetting, nd review of the resulting proof before it is published in its finl form. Plese note tht during the production process errors my be discovered which could ffect the content, nd ll legl disclimers tht pply to the journl pertin.

2 A Dynmic Multicst Tree bsed Routing Scheme without Repliction in Dely Tolernt Networks Yunsheng Wng nd Jie Wu Deprtment of Computer nd Informtion Sciences Temple University Phildelphi, PA Emil: {yunsheng.wng, Abstrct Dely tolernt networks (DTNs) re specil type of wireless mobile networks which my lck continuous network connectivity. Multicst is n importnt routing function tht supports the distribution of dt to group of users: service needed for mny potentil DTNs pplictions. While multicsting in the Internet nd in mobile d hoc networks hs been studied extensively, efficient multicsting in DTNs is considerbly different nd chllenging problem due to the probbilistic nture of contct mong nodes. This pper ims to provide non-repliction multicsting scheme in DTNs while keeping the number of forwrdings low. The ddress of ech destintion is not replicted, but is ssigned to prticulr node bsed on its contct rte level nd ctive level. Our scheme is bsed on dynmic multicst tree where ech lef node corresponds to destintion. Ech tree brnch is generted t contct bsed on the compre-split rule proposed in this pper. The compre prt determines when new serch brnch is needed, nd the split prt decides how the destintion set should be prtitioned. When only one destintion is left in the destintion set, we use either wit (no further rely) or focus (with further rely) to rech the finl destintion. The effectiveness of our pproch is verified through extensive simultions. Rtio-bsed-split performs best in the compre-split step, both in synthetic nd rel trces. Using the wit scheme cn reduce the number of forwrdings, while using the focus scheme cn reduce the ltency. Keywords: Contct, dely tolernt networks (DTNs), dynmic multicst tree, efficient protocols, multicst, opportunistic routing. Preprint submitted to Journl of Prllel nd Distributed Computing December, 0

3 A Dynmic Multicst Tree bsed Routing Scheme without Repliction in Dely Tolernt Networks Yunsheng Wng nd Jie Wu Deprtment of Computer nd Informtion Sciences Temple University Phildelphi, PA Emil: {yunsheng.wng, Introduction With the dvncement in technology, communiction devices with wireless interfces hve become more nd more universl. Recently, lot of dely tolernt networks (DTNs) [] technologies hve been proposed to llow nodes in such extreme networking environments to communicte with one nother. Dely tolernt networks re wireless networks where, most of the time, n end-to-end pth does not exist between some or ll of the nodes in the network. The nture of node contct is non-deterministic. These networks hve vriety of pplictions, including crisis environments such s: emergency response nd militry bttlefields, vehiculr communiction, nd deep-spce communiction. Severl DTNs unicst routing schemes hve been proposed [], [], [], []. However, hving n efficient delivery service for multicst trffic is eqully importnt. We cnnot directly pply the multicst pproches proposed for the Internet or well-connected mobile d hoc networks to DTNs environments becuse of the sprse connectivity mong nodes in DTNs. There hs lso been some work on multicst routing protocols in DTNs [], [], [], [], [0]. Existing work focuses on three models: () single node (lso clled ferry) model ([] nd []), in which one single node holds ll destintions nd delivers to ech destintion t contcts through movement; (b) multiple copies In DTNs, routes re comprised of cscde of time-dependent contcts (communiction opportunities) used to move messges from their origins towrd their destintions []. Preprint submitted to Journl of Prllel nd Distributed Computing December, 0

4 model ([] nd []), in which the destintion set is replicted t contct once certin condition relted to the qulity of the encountered node is stisfied; (c) single copy model [0], where single copy of ech destintion is mintined where destintions cn be scttered t different nodes. Ech destintion is forwrded to n encountered node if it hs higher contct frequency of reching the corresponding destintion. This forwrding rule is clled priority-bsed-split (PS) in this pper. Our scheme is bsed on the single copy model with the objective to rech destintions quickly while minimizing the number of forwrdings. We observe tht pure priority-bsed-split my produce n excessive number of forwrdings (e.g., for succession of smll improvements). We propose to use the node s ctive level together with the contct rte level to determine when nd how to split destintion set during contct. The notion of the ctive level is bsed on the observtion tht n ctive node hs better chnce of contcting higher priority node lter to improve its delivery time. More specificlly, we hve the following two notions: Contct rte level with respect to destintion: priori knowledge or estimtion of the number of contcts with the destintion in given period. Active level of node: priori knowledge or estimtion of the number of totl contcts in given period. In this pper, we propose compre-split scheme t ech contct during the construction of dynmic multicst tree. The first step is the compre prt. When node, with destintion subset, hs contct with node b without ny destintion subset, we set the condition for splitting s follows: split occurs when the sum of the contct rte levels for ll destintions ssocited with b is higher thn the one ssocited with. The second step is the split prt. We propose rtio-bsed-split (RS), which splits the destintion subset bsed on the ctive levels of two encountered nodes. We then present n optiml split lgorithm, which prtitions the destintion subset bsed on the clculted rtio such tht the combined sum of the contct rte levels t nodes nd b re mximized. When there is only one destintion in the messge holder s destintion set, we use two schemes to forwrd the messge to this destintion: () wit: wit until meeting the destintion; () focus: forwrd the messge to higher contct rte level node until rriving t the destintion.

5 The mjor contributions of our work re s follows: We propose the notions of contct rte level nd ctive level to guide the construction of multicst tree. We present compre-split rule to blnce the need to deliver the messge to multicst destintions quickly while keeping the number of forwrdings low. We develop n optiml split process t ech brnch of the multicst tree. We evlute the proposed scheme not only in synthetic trces, but lso in rel mobility trces. The simultion results show the good performnce of the compre-split scheme in DTN multicsting. The rest of this pper is orgnized s follows: Section reviews the relted work. Section is the preliminry work. Section presents n overview of our multicsting scheme. Section provides some other methods. Section nlyzes these protocols. Section focuses on the simultion nd evlution. We summrize the work in Section.. Relted Work Mny multicst protocols hve been proposed to ddress the chllenge of the frequent topology chnges in mobile d hoc networks [] nd []. In generl, there re two types of multicsting protocols: tree-bsed nd mesh-bsed. In tree-bsed pproches, either the source-tree-bsed (such s multicst extensions to open shortest-pth first (MOSPF) [], protocol independent multicst (PIM) [], distnce vector multicst routing protocol (DVMRP) [], nd multicst on-demnd distnce vector routing protocol (MAODV) []) or shred-tree-bsed (core bsed tree (CBT) []) pproches re used. The former one constructs multicst tree mong ll of the member nodes for ech source node; usully this is shortest pth tree. This kind of protocol is more efficient for the multicst, but hs too much routing informtion to mintin nd hs less sclbility. The ltter one constructs only one multicst tree for multicst group including severl source nodes. The mesh-bsed method, on-demnd muticst routing protocol (ODMRP) [], nd forwrding group multicst protocol (FGMP) [], re more robust through redundnt pths. Almost ll protocols re bsed on building n infrstructure (tree or mesh).

6 There hve been recent works which consider multicsting in DTNs. In the single node (lso clled ferry) model, one single node holds ll destintions nd delivers them to ech destintion t the contcts through movement. In [], Zho, Ammr, nd Zegur proposed the bsic single node model together with new semntics for DTN multicsting, which explicitly specify temporl constrints on group membership nd messge delivery. Yng nd Chuh [] presented two-stge single node model, where routes to destintions re first identified through ferry, followed by the messge delivery long the discovered routes. In [0], Wng, Li, nd Wu studied dynmic version of the single node model. Although there is only one single node tht holds ll destintions, the messge holder will only forwrd the messge to node tht hs higher qulity. This pproch is n extension of the delegtion forwrding [] used in DTN multicsting. In the multiple copies model, the destintion set is replicted t contct once certin condition relted to the qulity of the encountered node is stisfied. In [0], the messge holder (for prticulr destintion) will replicte copy to n encountered node tht hs higher qulity with respect to the destintion. The number of copies cn be controlled using ticket-bsed scheme []. In [], Lee et l. proposed RelyCst, routing scheme tht extends the two-hop rely lgorithm in the multicst scenrio, which considers the k-copy repliction scheme where pcket is replicted to k rely nodes. In [] nd [], the number of tickets (L initilly) is divided into hlves for ech forwrding. The single copy model is similr to the multiple copies model. The difference is tht the originl node does not mintin copy. Tht is, there is only one copy for ech destintion. In [0], Go et l. developed single copy model where the forwrding metric is bsed on the socil network perspective. In [] nd [], Spyropoulos et l. lso delt with the sitution of when the number of tickets is reduced to one: spry-nd-wit nd spry-nd-focus. In the spry phse, for every messge originting t source node, L messge copies re initilly spred - forwrded by the source nd possibly other nodes receiving copy - to L distinct relys. In the next phse, wit mens tht the holder will forwrd the messge only to its destintion, while focus mens messge cn be forwrded to different rely ccording to given forwrding criterion. In recent yers, biologists hve found tht Levy wlks cn be commonly used to describe the mobility ptterns of forging nimls [], [], []. Computer scientists lso pid ttention to this re of reserch. They stud-

7 ied Levy wlks in humn mobility [], [], [], which cn help us to nlyze wireless mobile networks such s DTNs. From [], in wireless mobile networks, humn mobility ptterns hve fetures defining Levy wlks; their flight distributions nd puse time distributions closely mtch truncted power-lw distributions. The men squred displcement (MSD) lso shows significnt influence on these mobility ptterns. In this pper, we first propose nd pply the destintion set splitting in DTN multicsting, which is bsed on the single copy model. Our methods re ll bsed on the tree structure (but not necessrily shortest in the contct grph) in order to reduce the number of forwrdings nd ltency. When there is only one destintion in the destintion set, we pply wit nd focus schemes in our solutions.. Preliminries.. Objectives The objective of this pper is to develop n efficient single-copy multicsting scheme in DTNs. Single-copy multicsting reduces the storge requirement of ech node. Two performnce metrics re used: () number of forwrdings: the number of forwrdings for whole multicst process. This cn be considered s the cost for the multicst process; () ltency: the verge durtion between messge s genertion nd the rrivl time t the lst destintion. Efficient multicst mens hving fewer number of forwrdings nd smller ltency... System Models Assume tht there re N nodes in the whole network. The destintion set of multicst is represented s D = {,,..., n}. Ech node is ssocited with contct rte vector (f, f,..., fn), where fi indictes the frequency tht node meets destintion i in given period T. fi is lso clled contct rte level for destintion i in period T. We use (c, c,..., c n) to indicte the number of times tht node meets destintion i in given period T. Hence, the contct rte level fi cn be presented s follows: A flight is defined to be longest stright line trip from one loction to nother tht prticle mkes without directionl chnge or puse. MSD is defined to be the vrince of the displcement probbility distribution. Here it is discrete probbility distribution.

8 C C T T Figure : An illustrtion of the system models. fi = c i T. () In order to involve the effect from recent informtion, we lso define T, which is considered s recent period. (c, c,..., c n ) indictes the frequency tht node meets destintion i in given period T. Hence, we define the contct rte level fi s follows: fi = w c i + ( w) c i c i () T T T where w is the weight of the recent informtion for the contct rte level. The ctive level of node : A is the number of totl contcts per time unit T tht node meets with ll other nodes in the network. A = N fi. () i= Fig. illustrtes the system models considering the recent informtion... Chllenges nd Min Ides Contct rte level indictes the contct frequency of reching prticulr destintion without further forwrding, while ctive level indictes the likelihood of contcting other nodes to enhnce the contct rte level through forwrding. The chllenges lie in the blncing of these two fctors when two nodes meet. In our single-copy multicst, the key is to decide when nd how split should occur in constructing multicst tree. In this pper, we propose compre-split scheme t ech contct during the construction of dynmic multicst tree. The first step is the compre prt, which determines when split should occur. When node, with destintion subset, hs contct with node b, without ny destintion subset, we set the condition for splitting s follows: split occurs when the sum of

9 encounter Destintion set {,,, m} { } Contct rte level Active level Contct rte difference vector { b } { f,,, } b f b f b m,,, f f f m A N = i = f i A b N = i = {d, d,, d m } d = f f i i i f b i b kth element prtition {d, d,, dm} {d ', d ',, d m '} split destintion set b Destintion set {,,, k } {(k+), (k+),, m } A k = m A + Ab Figure : An illustrtion of rtio-bsed-split. the contct rte levels for ll destintions ssocited with b is higher thn the one ssocited with. The second step is the split prt, which decides how split should be done. We propose rtio-bsed-split (RS), which splits the destintion subset bsed on ctive levels of two encountered nodes. We then present n optiml split lgorithm, which splits the destintion subset bsed on the clculted rtio such tht the combined sum of contct rte levels t nodes nd b re mximized.. Compre-split In this pper, we propose compre-split scheme t ech contct during the construction of dynmic multicst tree. In this section, we will present the two steps of this method nd give n exmple to explin the whole process. The first step is compre, which determines whether split should occur. The second step is split, which decides how split should be done... Compre The first step for our non-repliction multicsting scheme is compre. When node, with subset of destintions D D (s shown in Fig., m is the size of subset D of destintion set D, n is the size of destintion set D), hs contct with new node b, without ny destintion subset, node will first send D informtion to node b nd nodes, nd b exchnge their contct rte vectors, (f, f,..., f m) nd (f b, f b,..., f b m), upon their contct. m is the size of the subset D of destintion set D. After compring these two

10 Compre m m b fi > i= i= f i Split the destintion set N = fi i= A k A A + Ab = m Node keeps k nodes tht hve higher vlues thn, or equl vlues to, the kth lrgest element. Node b keeps k nodes tht hve lower vlues thn, or equl vlues to, the kth lrgest element. Figure : An illustrtion of compre-split. nodes sum of the contct rte levels for ll destintions, if m fi b i= > m fi, then go to the next split step. Note tht two rounds of exchnges re used. One round cn be sved by exchnging (f, f,..., f n) nd (f b, f b,..., f b n). (f, f,..., f m) nd (f b, f b,..., f b m) cn then be extrcted loclly... Split The second step is to split the destintion set. Suppose tht d i = f i f b i is clled the contct rte difference between nodes nd b for destintion i. The ctive levels A cn be denoted by the number of totl contcts tht node meets with ll other nodes. i= A = N fi () i=

11 0 The destintion set splitting is bsed on the rtio of two encountering nodes ctive levels. The rtio k cn be denoted s: A k = m () A + A b. Both nd b generte the contct rte difference vector (d, d,..., d m ). Find the kth lrgest element in O(m) opertions using generl selection lgorithm [0].. Node keeps k nodes tht hve higher vlues thn, or equl vlues to, the kth lrgest element. In the cse of tie, when two contct rte differences re equl, the node ID is used to brek the tie.. Node b keeps m k nodes tht hve lower vlues thn, or equl vlues to, the kth lrgest element. In step (), the optiml liner solution is used to find the kth lrgest element. The whole split process is shown in Fig.... Exmple Fig. illustrtes the whole process of our proposed compre-split method. Next we cn use Fig. s n exmple. Node, with subset of destintions D = {,,,, }, mkes contct with node b, without ny destintion subset. First, node sends D to node b, nd they exchnge their contct rte vectors: (f, f,..., f ) = (,,,, ) nd (f, b f, b..., f) b = (,, 0,, ). After the clcultions, we hve = nd fi =. fi b i= Hence, the sum of the contct rte levels for ll destintions ssocited with b is higher thn the one ssocited with. Then, we go to the second step. The ctive levels of node nd b re 00 nd 0, respectively. We first clculte the contct rte difference vector: (d, d,..., d ) = (,,,, ) nd rtio: k = A A +A b m =. Then, we use the selection lgorithm to find the third lrgest number in the contct rte difference vector, which is. After splitting the destintion set, node keeps destintions: {,, }, nd destintions nd will be ssigned to node b. The combined contct rte of node nd b is f + f + f + f b + f b = 0, which is lrger thn i=

12 destintion Active level 00 b 0 0 d - - encounter b {,,,, } { } rtio-bsed-split A k = m = A + Ab split b {,, } {, } Figure : An exmple of rtio-bsed-split. fi i= =. This mens tht using the compre-split lgorithm cn increse the contct frequency of meeting with the destintions. In contrst, the usul greedy wy of the splitting process is s follows: () possible split : node will keep the lrgest contct rte level destintions nd ssign ll other destintions to node b. In this exmple, node will keep destintions {,, } nd ssign destintions nd to node b. After this process, the combined contct rte of nodes nd b is f +f +f +f b +f b =, which is smller thn using the compre-split lgorithm; () possible split : node b will get the lrgest contct rte destintions, nd node keeps the rest. Hence, fter splitting, node keeps destintions {,, }, nd node b keeps destintions nd. After this process, the combined contct rte of nodes nd b is f + f + f + f b + f b =, which is lso smller thn the result we get from the compre-split lgorithm.. Implementtion & Extensions There re mny other methods tht cn be implemented in the compresplit rule. First, we will explin some conditions in the compre phse. Then, we provide three other schemes when splitting the destintion set: rndombinry-split (RBS), medin-binry-split (MBS), nd priority-bsed-split (PS). Finlly, we will present two methods: wit nd focus [], [], when there is only one destintion in the destintion subset.

13 Split rtio-bsed-split (RS) rndom-binry-split (RBS) medin-binry-split (MBS) priority-bsed-split (PS) Tble : Different split methods... Compre In the previous section, we use the threshold-bsed condition (when node b hs higher sum of the contct rte levels for ll destintions thn node, split will occur) in the compre step. Also, we don t hve to use ny conditions in the first step. We will compre these two methods in our simultion. Another method is: if node b lredy hs destintion subset, node nd node b will combine their destintion sets, then split. It will increse the number of forwrdings. We will lso compre this method with our scheme in our simultion... Split In the split step, we lso hve mny other schemes: binry-split (BS) (rndom-binry-split nd medin-binry-split) nd priority-bsed-split.... Binry-split (BS) In binry-split, we will not consider ctive level. The destintion split will be equl prtition. The BS process is shown in Fig. : nodes {, b, c, d, e} re rely nodes, nd nodes {,, } re destintion nodes. When one node meets destintion, it will first ssign this destintion to it nd then use the binry-split. rndom-binry-split (RBS): fter meeting with node b, node will give hlf of the destintion subset D to b rndomly. This mens node keeps m/ nodes, nd node b keeps m/ nodes. medin-binry-split (MBS): in RBS, messge holder prtitions the destintions rndomly. It my ssign destintion to node with smll contct rte level to this prticulr destintion. Hence, the multicst process will hve lrge ltency. We use nother equl prtition

14 {,,,} {,,, } {,,, } b c {, } {, } {, } {, } b d c b e {} {} {} {} {} {} {} {} Figure : A smple of binry-split. which is bsed on contct rte difference. We use the medin of medins lgorithm [0]: liner solution to find the medin of the contct rte difference vector. Then, node keeps m/ nodes tht hve higher vlues thn, or equl vlues to, the medin, nd node b keeps m/ nodes tht hve lower vlues thn, or equl vlues to, the medin. MBS cn be viewed s specil cse of RS when the ctive levels of two encounter nodes re pproximtely the sme.... Priority-bsed-split (PS) Another solution is for node to keep the destintions with their contct rte difference vlues higher thn 0 nd to ssign ll other destintions to node b. This mens tht only the destintions with higher contct rte levels in node b thn in node will be ssigned to node b. Priority-bsed-split is shown in Fig.. Initilly, node tkes destintions {,,..., }. In the split phse, the copy rrives t destintions {,, } nd destintions re ssigned to nodes {b, c, d, e, f, g}... Wit nd Focus When there is only one destintion tht is crried by node, we lso hve two strtegies for forwrding decisions, s in [] nd []: wit: Node will keep this destintion until it meets the prticulr destintion. focus: Node will ssign this destintion only to node which hs high contct rte vlue for this destintion.

15 {} {} {,,,} {,,,} d b {,,,, } {, } b { } {,,, } {, } {, } e d f {} {} { } {, } f {, } g c {} {} {} {} Figure : A smple of priority-bsed-split.. Anlysis In this section, we will explin the optiml split process t ech brnch of the multicst tree. Then, we nlyze the benefit considering contct rte level nd ctive level t the sme time. Finlly, we compre the difference mong single node, single copy, nd multiple copies models... Optiml Split Algorithm Our mjor gol in using the non-repliction multicsting scheme in DTNs is to ensure tht the delivery of multicst informtion is done over different pths. Ech pth hs reltively high contct frequency of reching the corresponding destintion subset quickly. Then, multiple holders for destintion nodes cn serch for destintions in prllel. These solutions cn reduce the multicst cost. The number of forwrdings is mjor metric to mesure the cost of the multicsting process. Compre-split cn lso reduce the ltency in DTN multicsting. Suppose tht D is the destintion subset kept in node nd tht D b is the destintion subset ssigned to b, we would like to mximize the combined contct rte of nd b s follows: mx{ i D i + j D b b j }. ()

16 Theorem. Suppose tht D nd D b re two subsets s result of kth element prtition. d i = fi fi b is clled contct rte difference between nodes nd b for destintion i. Mximum combined contct rte of visiting ny of the destintions within time period occurs when for ech i D nd j D b, d i d j. Proof. It is cler tht ny other prtition (including the optiml one) cn be generted through sequence of swps between two elements, one ech from D nd D b. We show tht ech swp will deteriorte the combined contct rte level. Suppose i in D nd j in D b re swpped. Bsed on condition d i d j, we hve fi fi b fj fj b, or fi + fj b fi b + fj. Note tht fi + fj b is the combined contct rte involving destintions i nd j, wheres fj b + fi is the combined contct rte fter the swp of i nd j. The theorem follows. This optiml split lgorithm cn prtition the destintions to nodes with higher contct rte levels; hence, it cn reduce the number of forwrdings nd ltency in DTN multicsting... Contct Rte Level nd Active Level Both the contct rte level nd ctive level cn be estimted bsed on pst contcts. In fct, ech mobile node cn strt with predefined defult vlue for both contct rte level nd ctive level. It then itertively enhnces its estimtes bsed on new contcts. In this prt, we nlyze the necessity using contct rte level nd ctive level together for compre-split. We will use multicst with two destintions, blck nd white nodes, s n exmple to illustrte. Initilly, node holds both destintions. Consider tht is ssocited with tpe T of sequence of numbered slots tht hold contcts node hs with other nodes. ) Cse : select T with four rndomly selected distinct slots - two for blck nd two for white. The process is clled node s T ssignment. To see the reson of hving the sme condition (both for contct rte level nd ctive level), it is still better to split both destintions between nodes nd b thn to let keep both. We compre the following two pproches. The completion time for the non-split cse is the mximum slot number of the first white node nd the first blck node in node s tpe (T ). The completion time of the split cse is the mximum slot number of the first white node s slot number in T nd the first blck node s slot number in b s tpe (T b ). The ltter hs shorter expected delivery time.

17 ) Cse : to view the importnce of the contct rte level during split, consider cse where T hs three blck slots nd one white slot, while T b hs one blck slot nd three white slots. Both nodes nd b hve the sme ctivity level, nd we cn esily extend the rgument from Cse to the fct tht it is better to split. It is obviously better to ssign the blck destintion to node nd the white destintion to node b. Therefore, the priority-bsedsplit lgorithm is importnt s ech node ( or b) will increse its chnce to rech the corresponding destintion directly, resulting in smller ltency. A lrger contct rte level will lso reduce the number of forwrdings s its contct rte level is more difficult to be surpssed. ) Cse : to view the importnce of the ctive level during split, consider T with two blck slots, two white slots, nd four red slots, nd T b with two blck, two white, nd no other slots. Although both nodes nd b hve the sme contct rte levels to both destintions, node is twice s ctive s node b. In this cse, hs contcts with non-destintion nodes (red slots) which my hve better contct with destintion or b. In other words, destintion(s) ssocited with will hve chnce to be forwrded to third node with better contct rte level to nd/or b. Therefore, it is better to ssign both destintions to node, ssuming the benefit from the ctive sttus outweighs the benefit from the split (s in Cse )... Single Node, Single Copy, nd Multiple Copies Models The single node model uses the minimum number of forwrdings (in fct, it is the sme s the number of destintions). The delivery rtio cn be n issue if the holder hs very low contct rte level to prticulr destintion. Improvement includes creting delegtion when n encountered node tht hs better contct rte levels to ll destintions. Like the single node model, the single copy model lso keeps one copy for ech destintion, but it llows mny holders. The number of forwrdings is moderte s ech copy is forwrded only when there is better condition (bsed on the contct rte levels). Ltency is n issue; however, it cn be esily trded with the delivery rtio s the destintion set is quickly prtitioned to subsets with only single node. Ech holder cn judiciously determine whether nd when to terminte delivery process. The multiple copies model includes flooding, which copies the destintion set t ech node encountered. It is the fstest pproch, but it incurs sufficient number of copies per destintion. The number of copies cn be controlled through delegtion (i.e., copy destintion set only to ones with

18 Trce Number of nodes Number of destintions Levy wlks model 00,,,, Gussin distribution model 00,,,, Intel trce - Cmbridge trce - Tble : Simultion prmeters better condition). It still hs N (N is the totl number of nodes in the network) [] number of forwrdings, even for destintion set with one destintion. TTL-bsed or ticket-bsed pproches cn control the number of copies, but it is still chllenge to hve good estimte for TTL nd ticket numbers to ssure delivery while controlling the number of copies. Excessive copies lso consume limited memory spce t ech node, which cn prevent nd limit the support of multiple flows.. Simultion In this section, we compre the performnces of the schemes we mentioned in the previous sections. Ech simultion is repeted,000 times in MATLAB. In our simultion, the 0 percent confidence intervl of ech result is within ± percent. The following metrics re clculted in our simultion.. Averge cost: the verge number of forwrdings for ll destintions to receive the multicst messge.. Averge ltency: the verge ltency for ll of the delivered destintions to receive the multicst messge.. Averge ltency verge cost: the verge ltency verge cost for ll of the delivered destintions to receive the multicst messge. We will compre the multicsting schemes both in synthetic nd rel trces... Simultion Methods nd Setting We hve used the trces, not only in synthetic mobility models, but lso from rel trces. We will compre the number of forwrdings, ltency, nd their product in ech trce. In this pper, we consider tht the given period T is the whole period, nd T is 0% of T. Our simultion is bsed on two situtions:

19 Y X Figure : Levy wlks model. Without considering recent informtion (N-RI): using equtions () nd () to clculte the contct rte level nd ctive level, which does not consider the recent period informtion; Considering recent informtion (RI): w = 0. in equtions () nd (), which gives more weight to the recent informtion.... Synthetic Mobility Models In the synthetic mobility models, we set up 00-node environment. We set up two synthetic trces: Levy wlks nd Gussin distribution models. () Levy wlks model: from the simultion results in [], Levy distribution with scle fctor c nd exponent α in terms of Fourier trnsformtion cn be defined s the following:

20 split No condition Threshold-bsed medin-binry-split (MBS-W) rndom-binry-split (RBS-W) rtio-bsed-split (RS-W) priority-bsed-split (PS-W) Tble : Compre-Split-Wit legend of simultion results split No condition Threshold-bsed medin-binry-split (MBS-F) rndom-binry-split (RBS-F) 0 rtio-bsed-split (RS-F) priority-bsed-split (PS-F) Tble : Compre-Split-Focus legend of simultion results f X (x) = π + e itx ct α dt, () where α is the Levy exponent for flight length distribution, which follows power-lw distribution: p(l), 0 < α. A power lw distribution of l l+α puse times is denoted by ψ( t p ) / t +β p, where β is the Levy exponent for puse time distribution, 0 < β. Ech time two nodes mke contct with ech other, we give contct time nd GPS ddress. In the Levy wlks mobility pttern, we set up the Levy exponent for flight length distribution α, which is, nd the Levy exponent for puse time distribution β, which is lso in our simultion []. Fig. shows the mobility pttern of Levy wlks. The ctive level nd contct rte levels cn be clculted from the generted trce. Becuse we pln to exmine the performnce of equl prtitioning, we set the destintion numbers s i, i {,,,...}. (b) Gussin distribution model: in this model, we first rndomly select node s ctive level bsed on Gussin distribution model with µ =, 000 nd σ =, 000. Once the ctive level of node is selected, the ctive level is prtitioned into contct rte levels to ll nodes. Suppose node s contct rte level to node b is k, then in s T, k slots re rndomly selected. The destintion number setting nd mesuring prmeters re the sme s the Levy wlks model.

21 0 Cost just consider new node consider 'old' node Ltency just consider new node consider 'old node' () Number of forwrdings (b) Ltency Figure : Comprison of two compre methods.... Rel Trces We use Intel nd Cmbridge trces [] in our simultion. These dt sets consist of contct trces between short-rnge Bluetooth enbled devices crried by individuls. () Intel trce: this trce includes Bluetooth sightings by groups of users crrying smll devices (imotes) for six dys in the Intel Reserch Cmbridge Corporte Lbortory. There is sttionry node, nodes which re corresponding to mobile imotes, nd nodes corresponding to externl devices. There re, contcts between these nodes. Their contcts re rndom nd the nodes ctive levels nd contct rte levels re lso rndom. In our simultion, we rndomly set one of these nodes s the source, nd we choose other different nodes s the destintions. The number of destintions is from to. We will mke comprisons of the number of forwrdings nd ltency in these different prtition models. (b) Cmbridge trce: this trce includes Bluetooth sightings by groups of users crrying smll devices (imotes) for six dys in the Computer Lb t University of Cmbridge. nodes re corresponding to imotes, while nodes correspond to externl devices. In totl, only imotes could be used to produce this trce. Others were suffering from hrdwre resets. There re, contcts between these nodes. Their contcts re rndom nd the nodes ctive levels nd contct rte levels re lso rndom. In our simultion, we set node s the source nd choose different nodes s the destintions. The number of destintions is from to. We will lso compre the number of forwrdings nd ltency, s in the Intel trce.

22 Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Levy wlks model: compre-split-wit in N-RI. Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure 0: Comprison in Levy wlks model: compre-split-focus in N-RI.

23 Cost Ltency.x0.x0.x0.0x0.0x0.0x k 0.0k 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k 0.0k Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Gussin distribution model: compre-split-wit in N-RI. Cost Ltency.x0.x0.0x0.x0.x0.x0.x0.0x0.0x0.0x Ltency*Cost 0k 00k 0k 0k 0k 0k 0k 0k 0k 0k () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Gussin distribution model: compre-split-focus in N-RI... Simultion Results... Compre As we mentioned in Section, if one node hs contct with node which lredy hs destintion subset, we propose nother method: tht these two nodes destintion subsets re combined together nd then split. From Fig., we cn see tht this method increses the number of forwrdings compred to our method tht just splits the destintion subset to new node; t the sme time, it cnnot reduce the ltency much. Hence, in the rest of this pper, we will not use this method. We compre the number of forwrdings, ltency, nd their product in multicsting schemes, s shown in Tbles nd.... Without considering recent informtion (N-RI) In this prt, we will compre ll schemes without considering recent informtion bsed on equtions () nd (). () Results in synthetic mobility models

24 Cost Ltency.x0.x0.0x0.0x0.0x0.0x0.0x0 Ltency*Cost 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Intel trce: compre-split-wit in N-RI. Cost Ltency.x0.x0.0x0.0x0.0x0.0x0.0x0 0 Ltency*Cost 0.0k 00.0k 0.0k 00.0k 0.0k () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Intel trce: compre-split-focus in N-RI. In the Levy wlks model, we compred the number of forwrdings, ltency, nd their product mong these solutions, s shown in Figs. nd 0. It shows tht RS hs the fewest number of forwrdings nd the shortest ltency mong these four schemes in ll conditions (using threshold or not, wit or focus). PS performs better thn the other two binry-split schemes, while MBS is better thn RBS. We use compre-split-focus with thresholdbsed condition in Figs. 0(), 0(b), nd 0(c) to explin. RS-F (Line ) hs bout % less forwrdings thn PS-F () nd % less thn MBS-F () from Fig. 0(). RS-F reduces the ltency by % from PS-F nd % from binry-split in Fig. 0(b). By compring the product of number of forwrdings nd ltency, we cn see from Fig. 0(c) tht RS-F performs better thn other schemes. Using the threshold-bsed condition to decide whether to split the destintion set cn reduce the number of forwrdings by bout.%. This mens using the threshold-bsed condition cn help the messge holder to meet higher contct rte nodes. Using the wit scheme cn reduce the number of forwrdings, while using the focus scheme cn reduce the ltency.

25 Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Cmbridge trce: compre-split-wit in N-RI. Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Cmbridge trce: compre-split-focus in N-RI. In the Gussin distribution model, RS nd BS perform better thn PS, s shown in Figs. nd. For exmple, when using compre-split-focus with the threshold-bsed condition, RS-F() hs the best performnce mong these four solutions. Compred with the number of forwrdings, it is % fewer thn MBS-F (),.% fewer thn RBS-F (), nd.% fewer thn PS-F () from Fig. (). In Fig. (b), we know tht RS-F hs % shorter ltency thn MBS-F, 0% shorter ltency thn RBS-F, nd % shorter ltency thn PS-F in this cse. RS nd MBS perform better, when compring the product of the cost nd ltency, thn the other two schemes both in compre-split-focus nd compre-split-wit in Figs. nd. Using the threshold-bsed condition cn reduce the ltency by bout.% nd reduce the number of forwrdings by bout.% from the no condition in the compre step. Using wit cn reduce the number of forwrdings by bout 0%, while using focus cn reduce the ltency by bout 0% when there is only one destintion in the destintion subset. (b) Results in rel trces In the Intel trce, RS hs similr number of forwrdings for ech des-

26 Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Levy wlks model: compre-split-wit in RI. Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Levy wlks model: compre-split-focus in RI. tintion s PS, but much shorter ltency, bout % shorter, from Figs. nd. RS performs better thn PS when considering the product of ltency nd cost, s shown in Figs. (c) nd (c). Using the threshold-bsed condition in the compre step cn reduce the number of forwrdings nd ltency. In the finl step, when we wnt to reduce the number of forwrdings, we cn choose wit, nd if we wnt to reduce the dely, we cn use the focus scheme. In the Cmbridge trce, RS nd PS hve similr performnces in Figs. nd. RS hs shorter ltency while PS hs fewer number of forwrdings nd smller product of ltency nd cost. These two schemes re both better thn BS.... Considering recent informtion (RI) In this prt, we will compre ll schemes by considering recent informtion, bsed on equtions () nd () where w is 0.. From Figs. nd, we cn see our design split schemes perform similrly s in N-RI, s shown in Figs. nd 0. However, we tke more into ccount recent informtion thn in other schemes, which cn provide more

27 Cost Ltency.x0.x0.x0.0x0.0x0.0x k 0.0k 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k 0.0k Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Gussin distribution model: compre-split-wit in RI. informtion to the Levy wlks model; hence, TI reduces the number of forwrdings by bout % nd the ltency by bout % s compred with other schemes. In Figs. nd 0, the results do not chnge lot from RI, becuse the recent informtion hs the sme contribution to the ctive level nd contct rte level s the long term informtion in the Gussin distribution model. From the rel trces, s shown in Figs.,, nd, we cn see our designed schemes perform similrly s in N-RI. At the sme time, in RI, the cost, ltency, nd their product re reduced compred with N-RI. This mens tht recent informtion cn present the nodes mobility pttern better thn the previously cquired informtion... Summry of Simultion Results We use non-repliction multicsting schemes in DTNs. In the Levy wlks model, RS is better thn BS s the ctive levels of the nodes vry significntly. Using RS cn ssign the destintions to high ctive level nodes, while BS does not consider the ctive levels. In the Gussin distribution model, RS is better thn PS s ctive levels of the nodes re more uniform. This phenomenon is pervsive. In two rel trces, the ctive levels vry significntly. It ppers tht the role of contct rtes nd ctive levels re both very importnt. Hence, using PS nd RS is better thn using BS. If the compre step with threshold is used before splitting the destintion set, the number of forwrdings nd ltency will both decrese. Tble shows the best split method in different models. When there is only one destintion in the destintion set, using the wit scheme cn reduce the number of forwrdings while using the focus scheme cn reduce the ltency. From the comprison of N-RI nd RI, we cn find tht the role of recent informtion is very importnt.

28 Cost Ltency.x0.x0.0x0.x0.x0.x0.x0.0x0.0x0.0x Ltency*Cost 0k 00k 0k 0k 0k 0k 0k 0k 0k 0k () Number of forwrdings (b) Ltency (c) Ltency Cost Figure 0: Comprison in Gussin distribution model: compre-split-focus in RI. Cost Ltency.x0.x0.0x0.0x0.0x0.0x0.0x0 Ltency*Cost 0.0k 0.0k 00.0k 0.0k 0.0k 0.0k () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Intel trce: compre-split-wit in RI.. Conclusion In this pper, we focused on developing non-repliction multicsting scheme in DTNs. Our compre-split scheme is bsed on the single copy model with the objective to rech destintions quickly while minimizing the totl number of forwrdings. We proposed using the node ctive level together with the contct rte level to determine when nd how to split destintion set during contct. The split will occur when the messge holder hs contct with node with the sum of the contct rte levels for ll destintions being higher thn the messge holder. In the split process, we used rtio-bsedsplit to split the destintion set, then compred it with rndom-binry-split, medin-binry-split, nd priority-bsed-split schemes. When there is only one destintion left in the destintion set, we used wit or focus to forwrd the messge to the destintion. We compred the performnce of these schemes both in synthetic trces nd in rel trces. Trce driven simultion results showed tht compre-split with rtio-bsed-split, which considers both the contct rtes nd ctive

29 Cost Ltency.x0.x0.0x0.0x0.0x0.0x0.0x0 0 Ltency*Cost 0.0k 00.0k 0.0k 00.0k 0.0k () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Intel trce: compre-split-focus in RI. Different models Levy wlks mode Gussin distribution model Two rel trces Best split method RS RS RS / PS Tble : Conclusion of simultion results levels, hs the best performnce. Compre-split-wit hs less forwrdings while compre-split-focus hs shorter ltency. We believe tht the results obtined from this pper present the first step in exploiting the destintion set split rule in single copy DTN multicsting. Future reserch cn benefit from our results by developing specific pplictions bsed on the provided schemes in DTNs. Acknowledgments This reserch ws supported in prt by NSF grnts ECCS 0, CNS 0, CCF 0, CNS 0, nd CCF 00. [] K. Fll, A dely-tolernt network rchitecture for chllenged Internets, in: Proc. of ACM SIGCOMM (00). [] A. Lindgren, A. Dori, O. Schelén, Probbilistic routing in intermittently connected networks, SIGMOBILE Mob. Comput. Commun. Rev. (00) 0. [] C. Liu, J. Wu, Sclble routing in dely tolernt networks, in: Proc. of ACM Mobihoc (00). [] C. Liu, J. Wu, Routing in cyclic mobispce, in: Proc. of ACM MobiHoc (00). [] C. Liu, J. Wu, An optiml probbilistic forwrding protocol in dely tolernt networks, in: Proc. of ACM MobiHoc (00).

30 Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Cmbridge trce: compre-split-wit in RI. Cost Ltency Ltency*Cost () Number of forwrdings (b) Ltency (c) Ltency Cost Figure : Comprison in Cmbridge trce: compre-split-focus in RI.

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33 Jie Wu is the chir nd professor in the Deprtment of Computer nd Informtion Sciences, Temple University. Prior to joining Temple University, he ws progrm director t Ntionl Science Foundtion. His reserch interests include wireless networks nd mobile computing, routing protocols, fult-tolernt computing, nd interconnection networks. He hs published more thn 0 ppers in vrious journls nd conference proceedings. He serves in the editoril bord of the IEEE Trnsctions on Computers, IEEE Trnsctions on Mobile Computing, nd Journl of Prllel nd Distributed Computing. Dr. Wu is progrm co-chir for IEEE INFOCOM 0. He ws lso generl cochir for IEEE MASS 00, IEEE IPDPS 00, ACM WiMD 00, nd IEEE/ACM DCOSS 00. He lso served s pnel chir for ACM MobiCom 00. He hs served s n IEEE computer society distinguished visitor. Currently, he is the chir of the IEEE Technicl Committee on Distributed Processing (TCDP) nd ACM distinguished speker. Dr. Wu is Fellow of the IEEE. Yunsheng Wng received B.Eng. in Electronic nd Informtion Engineering from Dlin University of Technology, Dlin, Chin, in 00; the M.Res. in Telecommuniction from University College London, London, UK, in 00. He is currently working towrd the Ph.D. degree in the Deprtment of Computer nd Informtion Sciences, Temple University, US. His current reserch interests include routing in mobile d hoc networks (MANETs) nd dely-tolernt networks (DTNs).