Interference-Aware Multicast for Wireless Multihop Networks

Transcription

1 Intefeence-Awae Multicast fo Wieless Multihop Netwoks Daniel Letpatchya School of Electical and Compute Engineeing Geogia Institute of Technology Atlanta, Geogia Douglas M. Blough School of Electical and Compute Engineeing Geogia Institute of Technology Atlanta, Geogia Geoge F. Riley School of Electical and Compute Engineeing Geogia Institute of Technology Atlanta, Geogia Abstact In this pape, we evisit the poblem of optimal tee-based outing stuctues fo multicast in wieless multihop netwoks, but accounting fo the impact of intefeence. Ou analysis is based on the most accuate known intefeence model, namely the SINR-based physical intefeence model. We fist study the poblem in a low-intensity multicast scenaio whee we deive optimal node selection stategies fo diffeent subtee stuctues. We then extend these analyses to account fo intefeence between consecutive packets in highe-ate multicast scenaios. Based on these analyses, we popose and evaluate two new multicast outing stuctues: the intefeence-awae Steine tee (IAST) algoithm, which equies global knowledge of node locations, and the fixed-distance tee meging (FTM) algoithm, which does not equie global knowledge. We show that ou poposed algoithms povide up to 57% eduction in schedule length and up to 41% incease in goodput ove existing tee-based outing stuctues. I. INTRODUCTION In multicast, a single message is deliveed to a goup of destinations in a netwok. This poblem has been studied fo both wied and wieless netwoks. A suvey of multicast potocols fo ad hoc netwoks can be found in [1]. A majo limitation of eseach in this aea, to date, is that the vast majoity of woks ignoe intefeence, which is a significant facto in wieless multihop netwoks. The few woks that do conside intefeence use inaccuate models. In this pape, we cay out the fist eseach study of end-to-end multicast outing stuctues fo wieless multihop netwoks that accounts fo intefeence using accuate intefeence models. We design new intefeence-awae multicast outing stuctues and show that thei pefomance substantially exceeds that of existing multicast algoithms that do not account fo intefeence. Multicast outing appoaches can be classified into thee main categoies: tee-based, mesh-based, and stuctue-less. Tee-based potocols [2], [3], [4], [5] use diffeent kinds of tees as undelying outing stuctue to oute multicast messages to all destinations. Tee stuctues povide simple and cost effective outing infastuctues at the cost of obustness in the pesence of mobility and link failues. Mesh-based potocols [6], [7], [8] use mesh stuctues to povide obustness by having multiple outes between the souce and destinations at the cost of mesh stuctue maintenance. Stuctue-less multicast potocols do not explicitly ceate a outing stuctue but ely on othe methods such as netwok coding [9], [10] and geogaphic outing [11], [12]. In this initial study of intefeence-awae multicast, we focus on tee-based potocols due to thei simplicity and cost effectiveness. Extending the analyses and concepts developed heein to mesh-based potocols is an inteesting topic fo futue eseach. Most tee-based potocols have been based on shotest path tees o Steine tees. The goal of shotest path tees (e.g. [3], [4]) is to minimize the distance between the souce and each destination, while the goal of Steine tees (e.g. [13], [14]) is to minimize the sum of the distances in the multicast tee. A few studies compaing these pedominant tee stuctues have been done. Ruiz and Gomez-Skameta [15] studied shotest path tees and Steine tees. The authos agued that Steine tee is not appopiate fo wieless netwoks and poposed that the poblem should be e-fomulated to minimize the cost in tems of the numbe of fowading nodes. They poposed a geedy heuistic algoithm, called, and showed that the poposed algoithm is able to educe the numbe of fowading nodes. Nguyen [16] evisited the study and evaluated the pefomance of shotest path tees, Steine tees, and the algoithm in tems of packet delivey atio. The autho showed that shotest path tees offe the best pefomance in tems of packet delivey atio. Howeve, neithe of these studies accounted fo intefeence in thei evaluations. Othe wok that studied multicast scaling law and stuctue ae [17], [18], [19]. The authos studied the asymptotic multicast capacity of multihop wieless netwoks. In [19], a comb stuctue fo multicast tees that achieves capacity in the ode sense was poposed. While the wok did account fo intefeence, they used the potocol model fo intefeence, which is not as accuate as the physical intefeence model, and they wee concened pimaily with asymptotic scaling esults, athe than best pefomance on finite netwoks. A numbe of studies conside the multicast poblem with diffeent goals such as enegy [20], [21], [22], cost of building and maintaining multicast tees [23], We do not study these issues in ou pape. Scheduling is an impotant aspect of wieless multihop netwoks with intefeence. Scheduling can incease netwok thoughput by letting devices access the channel in an odely

2 fashion instead of the moe consevative contention-based access. The only multicast scheduling woks of which we ae awae ae [24], [25]. Howeve, [24] is pimaily concened with powe contol and scheduling plays only a mino ole, while [25] only deals with one-hop (not end-to-end) multicast. In this pape, we conside the poblem of intefeenceawae multicast outing tee in wieless multihop netwoks, using an accuate physical intefeence model. Fist, we study the poblem fo low-intensity multicast. We classify nodes into diffeent classes and deive optimal intefeence-awae outing stategies fo each class. Based on those analyses, we popose a new multicast outing stuctue based on Steine tees fo the low-intensity case. Next, we conside a geneal multicast scenaio and popose a second new multicast outing stuctue that is not based on Steine tee. We evaluate ou poposed stuctues though simulation in both the TDMA and CSMA/CA settings. Simulation esults demonstate that, compaed to existing appoaches, ou poposed stuctues educe the schedule length up to 57% in TDMA netwoks and achieve up to 41% highe goodput in CSMA/CA netwoks. II. SYSTEM MODEL AND PROBLEM FORMULATION We conside a communication gaph G = (V,E), whee V is a set of all wieless nodes. An edge (u,v) E if and only if d(u,v) t, whee d(u,v) is the Euclidean distance between nodes u and v and t is the maximum tansmission ange. We ae given a multicast souce s V and a set of multicast destinations M V. The poblem is to constuct a multicast tee ooted at s that spans M, along with a patition of a set of non-leaf nodes in the multicast tee S 1,S 2,...,S k, whee S i is a set of feasible tansmissions with the given intefeence model. A feasible tansmission set is a set whee, if all nodes in the set tansmit to thei espective eceives at the same time, all eceives will successfully eceive the tansmissions. We call the patition S 1,S 2,...,S k a schedule with schedule length k. Ou goal is to constuct a minimum length schedule. We adopt the classical model fo adio signal popagation, which is efeed to as the log-distance popagation loss model. The adio signal stength at a distance d fom the tansmitte is given by P d α, whee P is the tansmission powe and α is the path loss coefficient. We assume that nodes ae not equipped with intefeence cancellation capabilities. In this pape, we conside the physical intefeence (PI) model [26]. In the PI model, intefeence fom all concuent tansmittes in the netwok, no matte how distant, is factoed into the signal-to-intefeence atio (SIR) value at the eceive. Specifically, the tansmission will be coectly eceived by the eceive if and only if the SIR value at the eceive is lage than the SIR theshold (SIR min ). III. INTERFERENCE-AWARE ROUTING FOR LOW INTENSITY MULTICAST In this section, we conside low intensity multicast, which is defined as a situation whee the time between two consecutive packets geneated by the souce is geate than the time it takes to delive one multicast packet to all destinations. We w 2 w d 1 θ u d v 1 v 2 Fig. 1. A banching node u banching into two paths. fist conside an ideal netwok whee we ae given a souce node s and a set of destination nodes M and we ae able to place exta nodes anywhee in the netwok when building a multicast tee. Ou goal is to constuct a tee ooted at s that spans M while taking intefeence into account. To achieve this, we classify nodes in a multicast tee into thee classes. Leaf nodes nodes with no child. Path nodes nodes with exactly one child. Banching nodes nodes with moe than one child. Accoding to ou classification, leaf nodes do not fowad data in the multicast tee and so they do not geneate intefeence. Futhemoe, along a single path, thee is no intefeence between nodes since thee is only one packet being tansmitted at a time. Thus, the optimal stuctue along a single path is fo each tansmission to tavel as fa as possible, i.e. to sepaate consecutive nodes by the tansmission ange. Next, we detemine optimal stuctues involving banching nodes, which ae non-tivial to analyze. A. Banching Nodes with Two Childen We fist conside a banching node u with two childen v 1 and w 1 as shown in Fig. 1. The distance of the fist hop fom u to v 1 and u to w 1 is d, whee d t. The fist tansmission fom u to v and w is done by using a multicast o boadcast. The second tansmissions fom v 1 to v 2 and fom w 1 to w 2 occu at almost the same time. The coss intefeence fom the concuent tansmission is given by P [ 2 +2d(1 cosθ)+2d 2 (1 cosθ)] α/2. Combining the eceived signal stength and the intefeence, we set SIR to SIR min and convet to decibel to get ) 0 = (1 10 SIRdB min 5α 2 +2d(1 cosθ)+2(1 cosθ)d 2. Solving the equation, we get = b 2 d whee b 2 = 1 cosθ + (cosθ 1)( ( SIRdB min 5α ) +cosθ) ( SIRdB min 5α ) The esult shows that the distance between nodes afte the banching point is popotional to the distance of the fist hop. Let i be the depth fom u and i be a distance between a node at depth i and a node at depth i + 1. Fo all i > 0, we can conside d as a sum of all j, whee 0 j < i, we get i 1 i = b 2 j = b 2 (b 2 +1) i 1 0, whee i t and 0 t j=0 This shows that the distance between v i and v i+1 gows as v i gets futhe away fom u until the distance eaches t,

3 Fig. 2. w 2 w 1 d θ = 2π 3 d s d v 1 u 1 v 2 u 2 A banching node s banching into thee paths. which is the tansmission ange and coesponds to the optimal distance fo the single-path case. B. Banching Nodes with Thee Childen Next, we conside a banching node s with thee childen u 1, v 1, and w 1 as shown in Fig. 2. Applying a simila analysis to the two-child case, we get = b 3 d whee b 3 = ( log 2+SIRdB min 5α ) 10log 2+SIRdB min 2(10 5α 1) Again, the distance between nodes gows as nodes get futhe away fom the banching node, albeit in a slightly diffeent manne. Hee also, the distance will eventually each the limit t. Using the peceding analyses, we pesent an appoximation algoithm to build a multicast tee. The algoithm applies diffeent outing stategies depending on which is the applicable case (single path, two-way banch, o thee-way banch). C. Intefeence-Awae Steine Tee Algoithm (IAST) Since the optimal outing stategies ae diffeent fo diffeent classes, ou goal is to use diffeent outing stategies fo diffeent classes when building a multicast tee. Howeve, one of the difficulties of applying the appoach is identifying whee banching should take place. Ou goal is to fist identify banching nodes locations and use diffeent outing stategies fo diffeent classes when building a multicast tee. The high level idea of the intefeence-awae Steine tee outing algoithm is as follows: we ae given nodes that must be connected in a multicast tee. These nodes ae the souce node and all the destination nodes. The fist step is to identify how these nodes should be connected in a tee. The algoithm uses a Euclidean Steine Tee appoximation algoithm to locate ideal Steine nodes in the netwok, using M {s} as input. We call the etuned Steine Tee a Steine Ovelay Tee since it shows the big pictue connections between nodes in the netwok. An edge between two nodes in the Steine Ovelay Tee suggests that the two nodes should be connected by a path in the oiginal gaph. Note that if we viewm {s} as a multicast goup. The multicast goup will have one Steine Ovelay Tee egadless of which node is a souce node. Fo each Steine node, the algoithm finds a eal node neaest to the ideal Steine node location to act as the Steine node. The algoithm consults the Steine Ovelay Tee to detemine if the cuent node should be consideed as the souce node, a path node, o a banching node. The algoithm. k u v Fig. 3. An infinitely-long, equally-spaced linea netwok. uses diffeent distances fo diffeent node classes based on the analyses in Sections III-A and III-B. Note that Steine tees contain only two-way banches and up to one thee-way banch (at the souce), meaning that ou analyses ae sufficient to handle all cases. IV. INTERFERENCE-AWARE ROUTING FOR GENERAL MULTICAST In this section, we conside a moe geneal multicast scenaio whee the souce node may begin tansmission of the next packet befoe all eceives have eceived the pevious packets. As a esult, thee may be moe than one application laye packet being fowaded in the netwok. Multiple application laye packets being fowaded in the netwok means that intefeence in the netwok will be highe than the low intensity multicast case. Since moe than one application laye packet may be pesented in the netwok, we ae unable to diectly apply the analyses fom Section III. The exta intefeence means that the distances between nodes must be shotened to allow fo concuent tansmissions. To tackle this poblem, we intoduce a scaling facto, f, to be used to scale down the distances analyzed fom the Section III. Ou goal is to find the most appopiate value fo the scaling facto f. A. Scaling Facto in Path Nodes Conside a linea path in one dimension with infinite length as shown in Fig. 3. If all nodes ae equally sepaated by a sepaation = t, then all links in the path ae on the edge of the SINR theshold and no concuent tansmission is possible. The schedule length in this case will be on the ode of the length of the path. This phenomenon is known as the black-gay link paadox [27]. Edges with distance exactly equal to the tansmission ange ae efeed to as black links, and they do not allow a single concuent tansmission, no matte how distant. Edges with distance slightly below the tansmission ange ae efeed to as gay links, and they do allow concuent tansmission, although the allowable spatial sepaation might be quite lage. Given the black-gay link paadox, if the sepaations between nodes ae scaled down to = f t, whee 0 < f < 1, it should be possible to have multiple nodes tansmit concuently. Suppose that the schedule length is k. Two consecutive tansmittes ae sepaated by a distance k. Conside a tansmission fom node u to node v, the total intefeence expeienced by v is given by [ i=1 P (ik+) α + ] P (ik ) α, The SIR at the eceive v can be obtained by combining the eceived signal stength and the total intefeence at v, the SIR at v is given by the equation

4 SIR(v) = i=1 1 ]. 1 1 i=1[ (ik+1) + α (ik 1) α The tansmission will be coectly eceived by v if and only if SIR(v) SIR min ; we get the following inequality: 1 [ ] 1 (ik +1) α + 1 (ik 1) α SIRmin 1. (1) We use the convegence integal test to the left hand side of (1) and get 1 (k +1) α + 1 (k 1) α + (k +1)1 α +(k 1) 1 α SIR 1 k(α 1) min. (2) Equation (2) shows that accoding to SIR, the schedule length of an infinitely-long equally-spaced linea netwok depends only on the path-loss coefficient and the SIR min. Thus, the scaling facto can incease spatial euse but Equation (2) shows that the schedule length will eventually convege. Fo the IAST algoithm, the goal of the scaling facto is to accommodate concuent tansmissions fom othe nodes. We scale down the distance used when building a multicast tee by a facto f instead of using distances diectly fom the analyses in Section III. Since the application of the scaling facto is not limited to IAST, we popose ou second intefeence-awae algoithm. B. Fixed-Distance Tee Meging Algoithm The IAST algoithm equies global knowledge of the netwok to appoximate a Euclidean Steine tee and identify candidates to act as Steine nodes. Ou second algoithm, the fixed-distance tee meging (FTM) algoithm, does not equie global knowledge of the netwok. The algoithm gows the souce tee by meging the souce tee with the neaest destination node until all destination nodes ae connected. The high level desciption of FTM algoithm is as follow. The algoithm takes a pefeed scaling facto (f p ) as an input, whee 0 < f p 1. The algoithm uses the same distance = f p t when building a multicast tee. Fo each destination node, the algoithm finds a shotest path in tems of hop counts fom the eceive to all nodes in the netwok. The algoithm now knows the destination node neaest to the souce tee. The algoithm gows the tee fom the souce tee towads the destination node by using the following citeia when selecting the next hop node. 1) the next hop node must be close to the destination node 2) if thee exist multiple next hop nodes, the algoithm picks the next hop node that is closest to all othe emaining destination nodes Afte the selected destination node is meged with the souce tee, the algoithm selects the next destination node neaest to the new souce tee and gows the tee towad the selected node until all destination nodes ae included in the 1 We assume that SIR min > 0, whee SIR min is in a linea atio. tee. In the case whee node density is too low and gowing the tee with = f p t is not possible, FTM gadually inceases until the selected node is successfully meged o = t. C. Scheduling Algoithm To accommodate the outing tee with diffeent distances fo diffeent node classes, we popose a modified vesion of GeedyPhysical scheduling algoithm [28], called Tee-Based GeedyPhysical. The idea of Tee-Based GeedyPhysical is to schedule all fowading nodes at the same depth in the same slot until no moe fowading nodes can be accomodated in the slot. Tee-Based GeedyPhysical then evets back to the oiginal GeedyPhysical. V. PERFORMANCE EVALUATION We evaluate ou algoithms in thee diffeent settings. Fist, we stat by evaluating ou algoithms in a low intensity multicast setting whee the analyses in Section III can be applied diectly. Next, we evaluate ou algoithms in a geneal multicast scenaio whee the analyses cannot be applied diectly and scheduling is equied. Finally, we also evaluate ou algoithms in a CSMA/CA setting whee nodes access the channel in a contention-based manne athe than with TDMA. A. Simulation Paametes and Assumptions We use ns-3.15 simulato to evaluate all algoithms. We use a physical model of g at the data ate of 6 Mbps in the simulation. All nodes use the tansmission powe of 40 mw and themal noise is computed at 290K. In all simulations, 2000 nodes wee unifomly distibuted in a deployment aea of 1000 m by 1000 m unless othewise noted. 2 We compae IAST and FTM against existing tee-based stuctues: [15], [16], and [19]. Fo IAST algoithm, we use GeoSteine [29] to find a Euclidean Steine Tee. All esults epoted ae aveaged fom 1000 simulations. B. Low Intensity Multicast We begin ou evaluation with a low intensity multicast scenaio. We vaied the numbe of multicast destination nodes fom 10 to 100. To pevent multiple nodes fom fowading packets at exactly the same time, we inseted andom delay between 0 µs and 1000 µs befoe nodes fowad packets to thei childen. We measued the delay between the time when the souce node tansmits the packet and the time when all destinations have eceived the packets. The simulation esults ae epoted in Fig. 4. As seen fom Fig. 4, the IAST algoithm has the lowest delivey delay among all algoithms, even though has the shotest distance between the souce and evey destination. has a lage numbe of nodes and this ceates moe contention in the netwok, which means that nodes have to delay thei tansmissions when the channel is sensed as busy. and both have even longe delays, because they have both longe paths and highe contention. 2 With g at 6 Mbps, tansmission ange is athe small and faily high node density is equied fo the netwok to be connected.

5 Delay (ms) Schedule length Fig IAST Numbe of multicast destinations End-to-end delivey delay fo low-intensity multicast Fig. 5. C. Geneal Multicast Scaling facto (f) IAST Schedule length vs. scaling facto In this set of simulations, we conside a geneal multicast application whee the application geneates packets faste than the time it takes to delive packets to all destinations. Thus, we use a scaling facto and scheduling in the algoithms. We fist evaluate the scaling facto since it is a significant paamete affecting IAST and FTM pefomances. In this simulation, the numbe of multicast destinations is fixed at 10. We vay the scaling facto fom 0.3 to 1.0 and collect the schedule lengths etuned by IAST algoithm. We did not use the scaling facto below 0.3 since the netwok became disconnected in some simulations. The simulation esults ae epoted in Fig. 5. Fig. 5 confims that using diffeent scaling facto affects IAST pefomance. If the scaling facto is too small, the exta nodes included in the multicast tee outweigh the gain of spatial euse. If the scaling facto is too lage, spatial euse is not possible. Howeve, pefomance is quite stable acoss a faily wide ange of scaling factos, e.g. 0.5 to 0.7. Based on this analysis, we have set the scaling facto to 0.7 in the emaining simulations. We now conside the schedule length poduced by diffeent multicast outing stuctues, including ou IAST and FTM stuctues. Fo these simulations, we vaied the numbe of destinations fom 10 to 100. Thee ae multiple possible combinations between outing and scheduling algoithms. IAST- GP efes to IAST outing combined with the GeedyPhysical scheduling, IAST-TGP efes to IAST outing combined with Tee-Based GeedyPhysical. Fo, and, we epot the esults fom GeedyPhysical only since the diffeence between GeedyPhysical and Tee-Based GeedyPhysical ae not statistically significant with 1000 simulations. The schedule length ae epoted in Fig. 6. The esults of Fig. 6 show that the schedule lengths of IAST and FTM ae substantially shote than,, and. FTM schedules ae appoximately half the length of schedules, 1/3 the length of schedules, and less than 1/4 the length of schedules fo highe numbes of destinations. The shote schedule lengths means that IAST (o FTM) can suppot moe tansmissions than othe stuctues within the same time peiod. As expected, and Schedule length Schedule length IAST-GP FTM IAST-TGP Numbe of multicast destinations Fig. 6. Schedule length vs. numbe of destinations IAST-GP 7 6 FTM 5 IAST-TGP Fig. 7. Numbe of nodes Schedule length vs. node density achieved thei espective goals of shotest aveage path length and minimum numbe of fowading nodes. Howeve, outes built by and mostly consist of black links that cannot be activated concuently with any othes. As a esult, most of the fowading nodes selected by and must be scheduled sequentially, which inceases the oveall schedule length. The pesence of black links is even moe poblematic in since the numbe of fowading nodes is not taken into account, esulting in a vey lage numbe of fowading nodes that must be scheduled sequentially. Fo stuctue, the igid stuctue of esults in longe schedule length. We also evaluate the pefomance of all algoithms with vaying netwok density. We kept the numbe of destinations at 10 and vaied the numbe of nodes in the netwok fom 500 to The minimum numbe of nodes could not dop below 500 nodes since the netwok becomes disconnected in some simulations with ou settings of g at 6Mbps. The schedule lengths ae epoted in Fig. 7. As seen fom Fig. 7, the schedule lengths of IAST and FTM algoithms incease as the node density deceases. This effect is paticulaly noticeable fo IAST, because the closest nodes to ideal Steine node locations can be quite fa, meaning that the tee stuctues begin to deviate significantly fom ideal Steine tees. Since FTM is not built on Steine tees, it is less susceptible to the lack of ideal node locations and its schedule length does not incease as damatically fo lowe node densities. Even at the lowest node density, FTM s schedule length is about 17% shote than s, almost 34% lowe than s, and moe than 55% lowe than s. D. Contention-based Channel Access Although in CSMA/CA netwoks, tansmissions cannot be pecisely scheduled, we hypothesized that the geate tansmission concuency facilitated by ou intefeence-awae algoithms would still tanslate into bette pefomance fo the CSMA/CA case. To evaluate this, we pefomed ns-3 simulations using the standad ns model. To pevent multiple nodes fom fowading packets at exactly the same

6 Goodput (Mbps) IAST FTM Numbe of multicast destinations Fig. 8. Goodput of diffeent potocols. time, we inseted andom delay befoe nodes fowad packets to thei childen. The andom delay was chosen unifomly between 0 µs and 1000 µs. We measued the maximum goodput and epot the esults in Fig. 8. Note that thee is no scheduling in this CSMA/CA simulation, thus, only one vaiation of IAST is epoted. As seen fom Fig. 8, IAST and FTM still outpefom and even without explicit scheduling. In IAST and FTM, concuent tansmission is possible while black links in and ae intoleant of even a small intefeence fom concuent tansmissions. The andom delay helps mitigate the poblem in and. Without the andom delay, and pefomance was even lowe than the epoted esults. Thus, ou intefeence-awae multicast outing stuctues pemit highe levels of concuency and this esults in significant pefomance benefits even without explicit scheduling. VI. CONCLUSIONS In this pape, we have studied the poblem of multicast outing and scheduling fo wieless multihop netwoks. We have classified nodes in multicast tees into diffeent classes and shown by analyzing an accuate physical intefeence model that diffeent classes equie diffeent outing stategies to poduce optimal schedules. Based on these analyses, we have poposed two joint outing and scheduling algoithms fo multicasting in wieless multihop netwoks. We have evaluated the pefomance of diffeent algoithms though simulation and shown that the poposed algoithms outpefom othe algoithms in tems of schedule lengths and goodput. VII. ACKNOWLEDGEMENTS This eseach was suppoted in pat by the National Science Foundation unde Gants CNS and CNS REFERENCES [1] L. Junhai, Y. Danxia, X. Liu, and F. Mingyu, A suvey of multicast outing potocols fo mobile ad-hoc netwoks, Communications Suveys Tutoials, IEEE, vol. 11, no. 1, pp , [2] E. Roye and C. E. 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