Load-aware multicast routing metrics in multi-radio multi-channel wireless mesh networks

Computer Networks 55 (2011) 2150–2167

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Computer Networks

journal homepage: www.elsevier .com/locate /comnet

Load-aware multicast routing metrics in multi-radio multi-channelwireless mesh networks

Fangmin Li a, Yilin Fang a,⇑, Fei Hu b, Xinhua Liu a

a School of Information Engineering, Wuhan University of Technology, Wuhan 430070, Chinab Box 870286, Electrical and Computer Engineering, University of Alabama, Tuscaloosa, AL 35487, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 March 2010Received in revised form 23 July 2010Accepted 28 February 2011Available online 6 March 2011Responsible Editor: L. Lenzini

Keywords:Wireless mesh networksMulticastRouting metricsMulti-radioMulti-channel

1389-1286/$ - see front matter � 2011 Elsevier B.Vdoi:10.1016/j.comnet.2011.02.020

⇑ Corresponding author. Tel.: +86 027 87290335.E-mail addresses: [email protected] (F.

edu.cn (Y. Fang), [email protected] (F. Hu), liuxinhua@

Efficient multicast routing metric is critical for one-to-many communications in wirelessmesh networks. The existing unicast routing metrics do not perform well in multicastdue to the distinctive differences between unicast and multicast routing in frame exchangemanners in the link layer. It is thus necessary to propose specialized routing metrics formulticast. The focus of this paper is to investigate multicast routing metrics in multi-radiomulti-channel wireless mesh networks. We first solve multicast throughput optimizationproblem in concurrent multicast flows and show that the throughput can be improvedby seeking the multicast route with lower channel congestion degree. Then, the multicastrouting metrics and protocol are designed by considering this aspect. The main contribu-tion of our work is to propose two load-aware multicast routing metrics named FLMMand FLMMR. Both metrics account for channel diversity, interference and wireless broad-cast advantage. FLMM aids in finding multicast route that are better in terms of reducedintra-flow and inter-flow interference and exploits channel diversity to improve band-width usage and network throughput. Compared with FLMM, FLMMR further considersthe unreliability of MAC multicast. The effectiveness of the two metrics is empiricallyexamined through simulations. Finally, we present the further work from two aspects:the joint multicast routing and channel assignment problem for optimal multicast andthe practicality of proposed metrics.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Wireless mesh networks [1] (WMNs) have drawn sig-nificant attention in recent years due to their low mainte-nance overhead and high data rates. These networksconsist of mesh gateways, mesh routers and mesh clients,where mesh routers are rarely mobile and may not havepower constraints. All mesh routers form the backbone ofWMNs. The unique network feature brings many advanta-ges to WMNs such as large service coverage area, easy net-work maintenance, multi-band wireless device support,and network reliability enhancement. WMNs can provide

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Li), [email protected] (X. Liu).

broadband wireless services for various applications inurban, rural, and campus areas.

Multicast is a different routing service compared withunicast. The advantage of multicast is its efficient savingsin bandwidth and network resources since the mesh gate-way node can transmit the data with a single transmissionto a group of receivers [2]. Recently, many commercial mul-ticast-based applications are deployed in WMNs, such aslarge-scale audio/video conferencing, long-distance educa-tion, distributed interactive games, etc. These applicationshave high requirements in network capacity, real-timeproperty and transmission quality. Thus, it is necessary touse efficient multicast routing metrics and protocols tosupport these high-performance multicast-based applica-tions. This is very challenging considering the limitedcapacity of WMNs.

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F. Li et al. / Computer Networks 55 (2011) 2150–2167 2151

The reduction in total capacity due to interference inmulti-hop wireless networks is a critical factor influencinghigh-performance multicast routing design. Unlike othertypes of multi-hop wireless networks, WMNs allow moreflexible physical layer design to alleviate this problemdue to the limited mobility and the rechargeable character-istic of its mesh routers. With significant advances in phys-ical layer technologies, one approach for enhancing thenetwork capacity is to adopt the multi-radio multi-channel(MR-MC) architecture, where each node is equipped withmultiple radios and can use multiple orthogonal channels.By operating these radios in orthogonal channels, thetransmission concurrency can be significantly increased.Then, the network capacity can be enlarged and the poten-tial of supporting high-performance multicast-based appli-cations can be greatly improved.

Routing metrics in MR-MC WMNs should be designedto take advantage of the spatial reuse and transmissionconcurrency from multiple channels. We also have to con-sider and avoid some potential problems such as unfairallocation of bandwidth and topology partition caused byirrational usage of channel [3,4]. Besides, there are multi-ple concurrent multicast flows in the realistic networkenvironment. Due to the shared nature of wireless med-ium, these multicast flows interfere with each other, whichcause free competition of network bandwidth resource. Itis very likely that the bandwidth cannot be guaranteedwhen the network is under the heavy traffic load [5].Therefore, the practical design of multicast routing metricsshould target the following goals: reducing interference,balancing bandwidth utilization, improving total multicastthroughput and network load capacity for the multiplemulticast flows. How to fully exploit channel diversity inMR-MC WMNs to accomplish these goals is a critical issuein designing multicast routing metrics. In recent years, theunicast routing metric has been widely studied, but re-search on multicast routing metric in WMNs is still in itsinfancy. Due to the difference between unicast and multi-cast and the realistic network environment, existing rout-ing metrics may not be applied to our multicastframework. We need a new multicast routing metric, de-signed from the ground-up for concurrent multicast flowsin MR-MC WMNs.

In this paper, we address the design of load-aware mul-ticast routing metric for MR-MC WMNs. We first seek toderive a complete mathematical model of MR-MC WMNs,and formulate mathematical program for solving the mul-ticast throughput optimization problem in concurrentmulticast flows scenario. Our analysis indicates that the to-tal throughput and the network load capacity for multiplemulticast flows (or, equivalently, the total admissible vol-ume of multicast flows) can be improved through seekingthe multicast route with lower channel congestion degree.Based on this intuition, we propose two load-aware multi-cast routing metrics named flow load multicast metric(FLMM) and reliable flow load multicast metric (FLMMR).Both metrics account for channel diversity, interferenceand wireless broadcast advantage (WBA). WBA refers totransmissions from a node can be received concurrentlyby the neighbors within its communication rage. FLMMaids in finding multicast route that are better in terms of

reduced intra-flow and inter-flow interference and exploitschannel diversity to improve bandwidth usage and net-work throughput. Compared with FLMM, FLMMR furtherconsiders the unreliability of MAC multicast. We alsoincorporate our metrics and new support for MR-MCWMNs in the multicast ad hoc on-demand distance vector(MAODV) protocol [6] to design an enhanced MAODV-MRmulticast routing protocol. We study proposed metricsthrough extensive simulations, and show their effective-ness by comparing them with related routing metrics. Fi-nally, we further discuss the joint routing and channelassignment problem for optimal multicast throughput inMR-MC WMNs, and formulate a liner integer program forsolving this cross-layer optimization problem. Moreover,the practicality of our metrics is analyzed. We also presentthe variations of our metrics for multicast routing underthe assumption of physical interference model.

The remainder of the paper is organized as follows. Sec-tion 2 reviews the various routing metrics and multicastrouting protocols. Section 3 presents the design goal, sys-tem model, multicast optimization problem and the designof new metrics. In Section 4, we present the design of mul-ti-radio multicast routing protocol based on MAODV andour metrics. We show the simulation-based evaluation ofthe proposed metrics in Sections 5 and 6. Section 7 con-tains our further discussions about the joint multicastrouting and channel assignment problem for optimal mul-ticast and the practicality of routing metrics. Finally, Sec-tion 8 concludes our work and outlines future directions.

2. Related work

2.1. Routing metrics

The design of routing metrics has a great impact on theproper operation of routing protocols. It must accuratelycapture the quality of transmissions according to the appli-cation demand and characteristic of its target network andaid in computation of good quality routes. In MR-MCWMNs, a good routing metric can reflect some of the de-sired characteristics such as path length, available channelcapacity, level of interference, link quality and channeldiversity, etc. In addition, there are other basic criteria tojudge a routing metric, such as stability, agility, isotonicityand monotonicity.

Recently, most of the research on multi-hop routingmetrics is based on unicast routing. The expected trans-mission count (ETX) metric [7] characterizes the link lossratio. ETX is the expected number of MAC retransmissionsneeded to successfully deliver a packet from the sender tothe receiver. The ETX of a path is defined as sum of ETX ineach link along the path. It favors paths with higherthroughput and lower number of hops. But it does not con-sider the data rate at which the packets are transmittedover each link. The expected transmission time (ETT) met-ric [8] is an extension of ETX which considers the data rateused by each link. ETT is expected time to successfullytransmit a packet at the MAC layer. Both ETX and ETT donot consider the presence of multiple channels. Therefore,they find paths with less channel diversity. Also ETT

2152 F. Li et al. / Computer Networks 55 (2011) 2150–2167

characterizes the expected transmission time in the ab-sence of interference in the network. To find paths withless intra-flow interference, Draves et al. [8] proposed met-ric of weighted cumulative expected transmission time(WCETT) which is a weighted cumulative path metricusing ETT. WCETT comprehensively considers link quality,link capacity and channel diversity. But all links on thesame channel of the assumed paths will interfere witheach other. This will result in the selection of sub-optimalpaths and it does not reflect inter-flow interferences.Moreover, WCETT is not isotonic. The interference andchannel switching (MIC) metric [9] is designed to improveupon WCETT by considering inter-flow interference. It con-siders both inter-flow and intra-flow interference, and itcan be made isotonic if the nodes are decomposed into vir-tual nodes while applying minimum weight path findingalgorithms such as Dijkstra’s algorithm. However, theinterferences it calculates in saturation state cannot ensurethat the precise network interference distribution isgained. Based on the physical interference model, Subra-manian et al. [10] proposed interference aware routingmetric (iAWARE) for MR-MC WMNs to reflect both inter-flow and intra-flow interference. iAWARE uses the signalto interference and noise ratio (SINR) to measure the inter-ference between each other, and thus can reflect the linkquality, rate diversity and interference. However, com-pared with interference property, it favors links with lowerETT. In addition to the above-mentioned metrics, the exist-ing unicast routing metrics also include the adjusted ex-pected transfer delay (AETD) metric [11], the bottlenecklink capacity (BLC) metric [12], the contention-awaretransmission time (CATT) metric [13], etc.

Until now, only a few high-performance multicast rout-ing metrics have been proposed. Roy et al. [14] studied thelink-quality multicast routing metrics in single-radio sin-gle-channel (SR-SC) WMNs. They pointed out the differ-ence between unicast and multicast routing, andproposed five improved multicast routing metrics such asthe success probability product (SPP) metric. Zhao et al.[15] assumed that MAC layer multicast has retransmis-sion-based reliability and proposed the expected multicasttransmissions (EMT) metric based on this assumption. Theproposed metric can simultaneously reflect channel qual-ity and the WBA of wireless transmission. Up to this pointthe research on high-performance multicast routing met-rics for MR-MC WMNs has not attracted many attentions.

Apart from the design work of routing metrics men-tioned above, Yang et al. [16] presented a systematic re-search of the relationship between routing metrics androuting protocols. The relationship between isotonicity ofmetric and lightest paths is analyzed, and properties fordifferent routing protocols are studied. Their analytical re-sults provide useful guidelines for understanding the de-sign space of routing metric in different routing protocols.

2.2. Multicast routing protocols

Recently, there has been a lot of research on multicastrouting protocols for SR-SC WMNs. Ruiz et al. [17] pre-sented the idea that the number of transmissions can beused as the metric to construct multicast tree. Their heuris-

tic algorithm can effectively use the WBA of wireless trans-mission. Therefore, it can reduce interferences andbandwidth consumption to certain extent. Murthy et al.[18], however, tried to improve multicast throughputthrough minimizing intra-flow interference. Their algo-rithm uses the self-pruning strategy to traverse all nodesto find multicast forwarding nodes. This strategy can effec-tively reduce intra-flow interference. But their centralizedmanner needs to know network topology and to scan allnodes. The efficiency of algorithm will be low when the net-work grows larger but the multicast group remains small.Zhao et al. [19] presented four polynomial time heuristicalgorithms aiming at providing multicast reliabilitythrough building node-disjoint paths. The method ofimproving reliability through redundant paths may incurlarge extra transmission overhead. Besides, it is very hardto fundamentally solve the problem of transmission unreli-ability by using the redundant paths at network layer. Toaddress this issue, Koutsonikolas et al. [20] studied multi-cast hop-by-hop reliability at the MAC layer and end-to-end reliability at the transport layer. It also improvesthe multicast reliability through some strategies such asthe usage of acknowledgments, retransmissions betweenneighboring nodes, the automatic repeat request betweeneach source–destination pair, and forward error correction.Apart from the above studies, lots of multicast routingprotocols in combination with the multi-rate nature ofthe network have been proposed. Broadcast incrementalbandwidth (BIB) algorithm and weighted connected domi-nating set (WCDS) algorithm [21] are two centralizedbroadcast tree construction algorithms aiming at reducingbroadcast latency and improving network throughput. Bothalgorithms consider the WBA and the multi-rate nature ofthe network, and also incorporate the possibility of multi-ple distinct-rate transmissions by a single node. But theyare not suitable for the networks with higher load becausethey are not aware of the dynamic traffic load. Qadir et al.[22] proposed three distributed and localized rate-awarebroadcast algorithms based on the connecting dominatingset (CDS). The distributed property of the algorithms helpsto improve their scalability. However, the algorithms aredesigned only for single-flow. In contrast, Liu et al. [23] con-sidered the more practical case of having multiple broad-cast or multicast flows present in a single-channel WMNs,and proposed two resource-aware tree construction algo-rithms which exploit the multiple link-layer rates, theWBA and the amount of available resources. The idea oftheir algorithms has certain similarity to ours, but theiralgorithms only apply to WMNs with a single shared chan-nel, which severely limits the network capacity.

There are also some multicast routing protocols forMR-MC WMNs. Li et al. [24] proposed multi-channel self-pruning (MCSP) routing protocol for broadcasting in MR-MC networks. Based on the localized interface-extendgraph, MCSP can decrease the transmission cost for net-work-wide broadcast by reducing the number of forwardchannels. Han [25] studied the problem of reducing broad-cast redundancy in MR-MC WMNs, and their approxima-tion algorithm can find a broadcast tree with lowerrelaying channel redundancy. The parallelized approxi-mate-shortest multi-radio multi-channel tree (PAMT)


algorithm [26] is proposed to minimize broadcast latencyin multi-rate MR-MC WMNs. PAMT extends the WCDS toadapt to the number of interfaces and channels available.It exploits the WBA, the multi-rate nature of the networkand the interface diversity on individual nodes. However,the centralized manner restricts the practicability of algo-rithm. In order to solve this problem, Qadir et al. [27] pro-posed a distributed and localized broadcast heuristicalgorithm that exploits the WBA, the multi-rate nature,interface diversity, and channel diversity. Simulation-based experimental studies show that this distributedalgorithm can provide low broadcast latencies close to thatof centralized PAMT. Besides, the work of Zeng et al. [28] isrelevant to the work presented in our paper. Their pro-posed algorithms perform multicast routing first, followedby channel assignment. They proposed dedicated load-aware channel assignment algorithm for multicast byusing the channel diversity. The channel assignment algo-rithm can use interference factors to minimize intra-flowinterference among one-hop neighbors, and can intelli-gently assign both overlapping and orthogonal channelsto nodes, but their multicast routing algorithms have noconsideration of the channel diversity. In contrast to theirwork, we focus on design of load-aware multicast routingmetric for multicast in MR-MC WMNs. Based on proposedmetrics, routing algorithm will select appropriate trans-mission path and channel to mitigate the effects of intra-flow and inter-flow interference among two-hop neighborsand fully exploit channel diversity to improve bandwidthusage and network throughput.

In addition, some multicast routing protocols used fortraditional multi-hop wireless networks provide refer-ences to the study of multicast routing for WMNs, suchas MAODV, etc. However, these protocols use hop counts(HOP) as routing metric, and thus cannot meet the high-performance requirements of multicast applications inWMNs. The protocol design needs to consider the uniquecharacteristics of WMNs and the application requirementsin practice.

3. Multicast routing metric for MR-MC WMNs

Packets are handled differently at the MAC layer in uni-cast routing and multicast routing [14], as shown in Fig. 1.The difference has direct implications on the design spaceand constraints of routing metric. Thus, the existing uni-cast routing metrics may not be applied to the multicastrouting. There are some multicast routing metrics for SR-SC WMNs, but they cannot reflect the channel diversity.Until now, the multicast routing metric in MR-MC has beenrarely studied. It is necessary to design proper multicast

Fig. 1. Comparison of packet exchanges at the MAC

routing metrics in combination with the unique character-istics of MR-MC WMNs and the multicast applicationrequirements in realistic network environment.

In this section, the design goal of multicast routing met-rics is presented firstly. Then, we seek to derive a completemathematical model of MR-MC WMNs, and formulatemathematical program for solving the multicast through-put optimization problem in concurrent multicast flowsscenario. Finally, two load-aware multicast routing metricsare designed based on the analysis results.

3.1. Design goal

The traffic patterns of WMNs determine the mesh gate-way and other key nodes will easily become traffic bottle-neck nodes. The routing protocols without considering thetraffic load of the concurrent multicast flows can easily re-sult in congestion, unfair bandwidth allocation and ineffi-cient use of network resources [5]. Therefore, maximizingthe network throughput and the network load capacityfor the multiple multicast flows (or, equivalently, the totaladmissible volume of multicast flows) is the primary goalof our multicast routing metrics to avoid hot spots and in-crease network utilization. This optimization is carriedout under the prerequisites that traffic demand of individ-ual flow and all network constraints can be guaranteed. Thisis actually a maximum concurrent flow problem (MCFP),i.e., multicommodity flow problem, in which every sessioncan send or receive flow concurrently [29]. For the MCFP, itis desired to assign flow to each route, such that the ratio ofthe flow supplied each session to the traffic demand of thatsession is the same for all sessions. The MCFP objective is tomaximize the network throughput, subject to all indispens-able constraints. In order to achieve this goal, it is necessaryto analyze the relationship between network throughputand distribution of multiple multicast flows, seek the com-plete constraints for multicast routing, and address theproblem of how individual multicast flows should be routedto maximize the network load capacity and the total net-work throughput. Due to the network-wide interferencesand the unique characteristics of MR-MC WMNs, the taskof finding optimal multicast route becomes considerablymore complicated.

3.2. System model

We focus on the optimal multicast routing for MR-MCwireless mesh backbone networks composed of wirelessrouters. We present the backbone networks as a directedgraph G = (V,E), where V is the set of routers and E isthe set of directed links each connecting a pair of routers

layer during unicast and multicast routing.


(suppose all are bidirectional links). There are jCj orthogonalchannels available, and each router node vi 2 V is equippedwith j(vi) (j(vi) 6 jCj) half-duplex radios for data transmis-sion. Each radio sends data through omni-directional an-tenna. We assume that all router nodes have the uniformtransmission range denoted by dT. The transmission ragedT represents the maximum distance up to which a packetcan be received.

For the sake of highlighting multicast performanceimprovement brought by routing metric, it is assumed thatthe channel assignment is done independently from multi-cast optimization framework. Our multicast approach per-forms channel assignment first, followed by multicastrouting. For any node vi on V, the system independently as-signs channel cj(vi) 2 C (1 6 j 6 j(vi)) for each radio on it.We stipulate that j(vi) channels assigned to the nodesare different from each other in order to fully exploit net-work channel diversity, that is cj(vi) – ck(vi), "j – k. Thechannel set assigned to node vi is expressed as C(vi) ={cj(vi)j1 6 j 6 j(vi)}. Let kv i � v jk be the distance betweenvi and vj (vi,vj 2 {v1,v2, . . . ,vn} = V) on V. If and only ifkv i � v jk 2 dT and channel ck 2 C(vi)

TC(vj) – ;, the corre-

sponding link eij(ck) 2 E exists, in other words, withoutinterferences in the neighboring area on channel ck, nodevi can successfully transmit data to node vj by using chan-nel ck. Meanwhile, vi and vj are adjacent nodes, and thetransmission rate of vi on channel ck is defined as R(vi,ck)bits/s.

In MR-MC WMNs, the multicast transmissions in thesame channel are subject to location-dependent interfer-ence. We determine the interference relationships be-tween all of the multicast transmissions in MR-MCWMNs based on the protocol interference model. It isassumed that the 802.11 MAC is used to conduct channelaccess. Packets are handled differently at the MAC layerin unicast and multicast routing, and the judgement condi-tions of multicast routing interferences are not the same asunicast. For unicast routing, the busy/idle state of medium

Fig. 2. Single MAC transmission potential interfer

is determined by both physical carrier-sense and virtualcarrier-sense mechanisms. The receiver will send clear tosend (CTS) frame and acknowledgment (ACK) frame tothe source. Therefore, the potential interference area ofMAC unicast should simultaneously include interferencearea of source and receiver, as shown in Fig. 2(a). In con-trast, multicast data frame is handled by using basic accessprocedure. Regardless of the length of the frame, no ex-change of request to send (RTS) and CTS frames shall beused. In addition, no ACK shall be transmitted by any ofthe recipients of the frame. Therefore, for multicast rout-ing, the potential interference area is only related to theset of receivers. Fig. 2(b) shows the maximum potentialinterference areas of a MAC multicast.

We assume that all mesh nodes have the uniform inter-ference range and denote the interference range of a meshnode as dI = (1 + D)dT, where D P 0 is a constant factor. Theinterference range dI represents the maximum distance upto which a node sensing the channel detects an ongoingtransmission. There exists interference between two MACmulticasts, if and only if these two MAC multicasts usethe same channel and at least a receiver of one MAC mul-ticast falls into the interference area of the other one’s sen-der (jdj 6 dI). Then they can not be active simultaneously.To model the wireless interference between the differentMAC multicasts of MR-MC MWNs, we define a conflictgraph, whose vertices correspond to the MAC multicastsin the communication graph, G. We draw an edge in theconflict graph between two vertices if one vertex interfere(or, equivalently, cannot occur simultaneously) with theother. Note that the interference effects between two ver-tices are not symmetric. Also note that we do not draw anedge from a vertex to itself in the conflict graph.

Suppose the set of multicast sessions that the networkcan effectively load is S, then Si = (vi,Ui, l(Si)), i = 1, . . . ,M.Here, vi 2 V denotes the source node of a multicast sessionSi, Ui # V � {vi} stands for the set of destination nodes, andl(Si) denotes the flow rate demand corresponding to Si. If

ence areas of unicast and multicast routing.


the network can effectively load S, it indicates that thesource node vi in any Si (Si 2 S) can successfully transmitT � l(Si) bits data to its set of destination nodes Ui in a periodof the schedule [(i � 1)T, iT] (T <1). Unlike the link-basedtransmission, each multicast session is comprised of agroup of MAC multicasts, which respectively correspondto a sender vj, the set of receivers denoted as N(vj,ck(vj),Si)and the channel used by this MAC multicast denoted asck(vj). The jth MAC multicast of Si is defined as the two-tuple in formula (1):

f ðv j; ckðv jÞ; SiÞ , ckðv jÞ;Nðv j; ckðv jÞ; SiÞ� �

; ð1Þ

where ckðv jÞ 2T

v l2Nðv j ;ckðv jÞ;SiÞCðv lÞ– ;.Our principal objective of the study on multicast rout-

ing metrics is to perform multicast routing to maximizethe total admissible volume of multicast flows and theoverall network throughput. Based on formula (1), thisobjective can be transferred into the seeking of the feasiblecombination of MAC multicasts for each Si in S under theconstraints of channel bandwidth, radio number and inter-ference between the close-by MAC multicasts in the samechannel. It can ensure that at least l(Si) amount of through-put can be routed for Si so that each f(vj,ck(vj),Si) can beinterference-free scheduled with the idealized transmis-sion scheduling strategy and the total admissible multicasttraffic load can be maximized. The key mathematical sym-bols used in this paper are tabulated in Table 1.

3.3. Metric design and analysis

According to the related definition in Section 3.2, themathematical program of the multicast throughput opti-mization problem in concurrent multicast flows scenariois given in this section. Let x(Si) be the stable transmissionrate of each multicast flow Si. Considering the bandwidthallocation fairness constraints between multiple simulta-neous multicast flows, for each Si, its stable transmissionrate should be proportional to its rate demand, that is:

xðSiÞP k � lðSiÞ; 8Si 2 S; ð2Þ

where k denotes the uniform scaling factor for all Si. Basedon the Inequality (2), it is known that the problem of

Table 1Index of mathematical symbols used.

G Communication graphV Set of nodesC(vi) Channel set assigned to vi

dT Transmission rangecj(vi) The jth channel assigned to vi

R(vi,ck) Transmission rate of vi in ck

Ui Destination node set of Si

x(Si) Transmission rate of Si

N Receiver set of fT Schedule periodX Transmission indicator variablek Load scaling factorTr(Si) Multicast tree of Si

Pð1ÞjProbability of successful MAC multicast

C(f,c) Channel assignment variableF(vi) Related MAC multicast set of vi

P Received power

seeking the maximum total multicast throughput withfairness constraints can be obviously transferred into theproblem of seeking maximum k under multiple constraints.In this way a network can ensure to transmit Si with therate of k � l(Si) bits/s (the lower bound).

In MR-MC WMNs, because of the limited number ofradios and the shared nature of wireless medium, thereare two major constraints which are described as follows:

(1) Due to the limit of radio number, node vi can be atmost assigned with j(vi) number of orthogonalchannels. As a result, the number of simultaneousMAC transmissions related to vi cannot surpassj(vi). Here, being related to vi means that vi is thesender or any receiver of a MAC multicast. Therelated MAC multicast set of vi is F(vi).

(2) Because of the shared nature of wireless medium,f(vj,ck(vj),Si) cannot be simultaneously transmittedwith the adjacent MAC multicasts on the same chan-nel. Here, being adjacent refers to these two MACmulticasts can not be active simultaneously.Namely, they share the common edge on the corre-sponding conflict graph. According to the relateddefinition of interference model in Section 3.2, theadjacent MAC multicast set interfering withf(vj,ck(vj),Si) can be denoted as I(f(vj,ck(vj),Si)).

The main research objective of this section is to analyzethe schedulability of each multicast flow under relatedconstraints and the relations between multicast routingthroughput and network bandwidth allocation. The pur-pose is to design effective metrics and aid multicast rout-ing protocols in computation of load-aware route.Because this paper is focused on the multicast routingstrategy at network layer, the optimal algorithms of chan-nel assignment and transmission scheduling will be ad-dressed in our future work. We assume that the networkis in the idealized interference-free transmission schedul-ing mode, and the system operates synchronously in atime-slotted model to control and schedule all MAC multi-casts in the networks. Time slot is defined as s, s = 1,2, . . . ,T. Here, T refers to a schedule period.

C Set of channelsE Set of linksj(vi) Radio number of vi

dI Interference rangeeij(ck) Link between vi and vj in ck

Si The ith multicast sessionl(Si) Traffic demand of Si

f MAC multicast transmissionI Interference set of fs Time slotd Channel congestion degreePHk Simple path between vk and source nodePjn Forward packet delivery ratio from vj to vn

P Error probability over the PHk

K(v,c) Channel assignment auxiliary variableF Set of MAC multicast in the networkx Physical interference weight


Based on time-slot model, we introduce a MAC multi-cast transmission indicator variable X(f(vj,ck(vj),Si),s), 1 6s 6 T which is assigned 1 if and only if f(vj,ck(vj),Si) is activein time slot s. Otherwise, the variable value is 0. Note thatequation X(f(vj,ck(vj),Si),s) = X(f(vj,ck(vj),Si),T + s) is satis-fied. Based on this indicator variable, the above-mentionedtwo kinds of constraints can be mathematically modeled asfollows:Xf ðv j ;ckðv jÞ;SiÞ2

Fðv iÞ

Xðf ðv j; ckðv jÞ; SiÞ; sÞ 6 jðv iÞ; 8v i 2 V 8s; ð3Þ

Xðf ðv j; ckðv jÞ; SiÞ; sÞ þX

f ðv j0 ;ckðv jÞ;Si0 Þ2Iðf ðv j ;ckðv jÞ;SiÞÞ

Xðf ðv j0 ; ckðv jÞ; Si0 Þ; sÞ

6 1; 8ckðv jÞ 2 C; 8s: ð4Þ

Node radio constraints are shown in Inequality (3) andMAC multicast congestion constraints in the same channelare shown in Inequality (4). For the impact of wirelessinterference, Jain et al. [30] pointed out that the transmis-sion feasibility can be analyzed through seeking all of theindependent sets of the conflict graph. This method cangive a set of necessary and sufficient conditions to ensurethe feasibility of multiple flows. However, the independentset constraints are computationally expensive and requireglobal information. Thus, they are not proper for use inpractice. Besides, two other methods, which only requirethe local information to determine whether a flow vectoris feasible or not based on row constraints or maximal cli-que constraints, are presented in [31]. Inequality (4) is de-rived from row constraints of MAC multicast conflictgraph. For a MAC multicast f(vj,ck(vj),Si), there is the prob-ability of parallel transmissions between the adjacent MACmulticasts in its corresponding I(f(vj,ck(vj),Si)). Therefore,for a feasible interference-free MAC multicast schedule,Inequality (4) is a sufficient but not necessary condition.

Since in every time slot that f(vj,ck(vj),Si) is active, thesender vj sends data to N(vj,ck(vj),Si) at rate R(vj,ck) onchannel ck. Therefore, x(Si) can be regarded as the averagerate attained on f(vj,ck(vj),Si) for channel ck during schedul-ing period T, that is:

xðSiÞ ¼Rðv j; ckÞ �

P16s6T Xðf ðv j; ckðv jÞ; SiÞ; sÞ

T: ð5Þ

The constraints in both Inequality (3) and (4) arerelaxed by using Eq. (5). And based on Inequality (2),the multicast throughput optimization in MR-MC WMNscan be formulated as the following linear programmingproblem (LPT):

max k

s:t: xðSiÞP k � lðSiÞ; 8Si 2 S;X

f ðv j ;ckðv jÞ;SiÞ2Fðv iÞ

xðSiÞRðv j; ckÞ

6 jðv iÞ; 8v i 2 V ; ð6Þ

xðSiÞRðv j; ckÞ

þX

f ðv j0 ;ckðv jÞ;Si0 Þ2Iðf ðv j ;ckðv jÞ;SiÞÞ

xðSi0 ÞRðv j0 ; ckÞ

ð7Þ

6 1; 8ckðv jÞ 2 C;k P 0; xðSiÞP 0; 8Si 2 S: ð8Þ

In LPT, the optimization goal is to maximize k under theconstraints of (2), (6), (7) and (8). Among them, Inequality(2) represents the traffic fairness constraints, Inequality (6)and (7) indicate the MR-MC WMNs node radio constraintsand the MAC multicast congestion constraints in the samechannel, respectively. This is a classical MCFP optimizationproblem. It is also a multicommodity flow problem inwhich all sessions can concurrently send or receive flowand it can be approximately solved by seeking the dualof primal problem with the method stated in [32].Although the optimal solution can be obtained theoreti-cally by solving LPT, this theoretical approach is not practi-cal to use in WMNs.

In MR-MC WMNs with coexistence of multiple multi-cast flows, the degree of congestion in congested areacan be reduced through reasonable network bandwidthallocation to realize network load balancing. In order tostudy the relations between multicast routing throughputand network bandwidth allocation, the network band-width allocation problems are analyzed with minimal de-gree of congestion. The channel congestion degree off(vj,ck(vj),Si) under MAC multicast congestion constraintsin the same channel is defined as:

dðf ðv j; ckðv jÞ; SiÞÞ ¼lðSiÞ

Rðv j; ckÞþ

Xf ðv j0 ;ckðv jÞ;Si0 Þ2Iðf ðv j ;ckðv jÞ;SiÞÞ

l Si0ð ÞRðv j0 ; ckÞ

: ð9Þ

Further, we define d = maxd(f(vj,ck(vj),Si)) as the maxi-mal degree of congestion (or, equivalently, the maximalchannel interference) in the network. The linear program-ming of bandwidth allocation problems with minimal de-gree of congestion (LPC) is then formulated as follows:

min d

s:t:X

f ðv j ;ckðv jÞ;SiÞ2Fðv iÞ

lðSiÞRðv j; ckÞ

6 jðv iÞ � d; 8v i 2 V ð10Þ

lðSiÞRðv j; ckÞ

þX

f v j0 ;ckðv jÞ;Si0ð Þ2Iðf ðv j ;ckðv jÞ;SiÞÞ

l Si0ð ÞRðv j0 ; ckÞ

; ð11Þ

6 d; 8ckðv jÞ 2 C;

d P 0; lðSiÞP 0; 8Si 2 S: ð12Þ

In order to reveal the relation between multicast rout-ing throughput and bandwidth allocation, we let d = 1/kand x(Si) = k � l(Si). It is easy to derive that LPC is equivalentto LPT. Namely, we can seek multicast route with lower de-gree of congestion for individual multicast flow to balancenetwork bandwidth utilization. It also ensures that anymulticast flow uses the minimally network bandwidth re-sources. Then the total multicast throughput and the net-work load capacity for the multiple multicast flows canbe improved. Based on this intuition and combined withthe transmission characteristic of MAC multicast, we pro-pose a load-aware multicast routing metric to improvenetwork throughput and load capacity as follow:

FLMMðv j0 ; SiÞ ¼ dðf ðv j; ckðv jÞ; SiÞÞ �1

jNðv j; ckðv jÞ; SiÞj;

v j0 2 Nðv j; ckðv jÞ; SiÞ ð13Þ


On the right side of Eq. (13), the first component is in-spired by the optimization objective function of LPC, andit indicates the channel congestion degree of related MACmulticast. The second component reflects the WBA of wire-less transmission. Thus, FLMMðv j0 ; SiÞ represents the addi-tional average congestion degree of v j0 for multicastsession Si when v j0 joins related MAC multicast. And thechannel congestion degree of f(vj,ck(vj),Si) is determinedtogether by all of the receivers in N(vj,ck(vj),Si). It is known,from the cost function of channel utilization proposed in[33], that the higher degree of channel congestion it has,the more packet loss ratio and the lower throughput it willbe. As the degree of channel congestion increases, the traf-fic transmission cost becomes more expensive with anapproximate exponent. The proposed multicast routingmetric can balance network bandwidth utilization andrealize the reasonable allocation of multicast flows be-tween all channels in the whole network. Therefore, itcan also reduce the traffic transmission cost.

The effectiveness of proposed metric is further dis-cussed. Due to the stationary nature of mesh routers, themost multicast routing approach designed for WMNs isbased on least-cost path tree. Each source–destination pairin the multicast session has only one simple path on thetree. The simple path PH is computed, whose cost is thesum of the costs of the links along the route. All of thepaths are then merged to form a multicast tree Tr. Hence,the path metric calculation problem needs to be analyzed.

For a destination node vk 2 Ui, the simple path betweenit and the source node vi is defined as PHk. Let Vk be the setof tree nodes on the PHk. It is easy to derive that the addi-tional congestion degree of PHk is as follow:

Fig. 3. Example showing the isotonicity and monotonicity of FLMMR.

FLMMðPHkÞ ¼X

v j0 2Vk� v if gFLMMðv j0 ; SiÞ: ð14Þ

Clearly, based on the multicast data distribution charac-teristics and the WBA of wireless transmission, Eq. (14) re-flects the upper bound of additional congestion degreecaused by PHk. Besides, since the aggregate path cost isthe sum of each FLMM(vj,Si), and each FLMM(vj,Si) is non-negative, it is easy to derive that FLMM has strict isotonic-ity and strict monotonicity [16].

As previously stated, in order to guarantee the wideapplication of metrics proposed in this paper, we assumethat the widely-applied 802.11 MAC is used to conductchannel access. However, this access mechanism cannotprovide multicast delivery reliability for the node to itsneighbors. Therefore, the influence that the probability ofsuccessful packet transfer of PHk has on the multicast per-formance also needs to be considered.

For a tree node vm 2 Vk � {vi} on the PHk, we say that itscorresponding MAC multicast is f(vj,ck(vj),Si), and vm 2N(vj,ck(vj),Si). For any node vn 2 N(vj,ck(vj),Si), the link pack-et delivery ratio of forward direction from sender vj to vn isdefined as Pjn. Because MAC multicast has no reverse trans-mission, the packet loss ratio from vj to vn can be directlyobtained as 1 � Pjn. Besides, since MAC multicast has nolink layer retransmission mechanism, its probability ofsuccessful MAC multicast is the probability of successfulmulticast data delivery without retransmission. It is assumed

that each of the nodes has an independent packet lossratio, the probability of successful MAC multicast isgiven by:

Pð1Þj ¼Y

vn2Nðv j ;ckðv jÞ;SiÞPjn: ð15Þ

We further assume that all MAC multicast transmis-sions on the PHk are mutually independent, and then theprobability of a transmission error over the PHk can beshown as:

P ¼ 1�Y

v j2Vk� v if gPð1Þj : ð16Þ

Because of the independence of each MAC multicasttransmission, it is guaranteed that the number of transmis-sions necessary to ensure the successful transfer of a pack-et is then a geometrically distributed random variable X,such that:

PðX ¼ kÞ ¼ Pk�1 � ð1� PÞ; 0 6 P 6 1; k ¼ 1;2; . . . ð17Þ

According to Eq. (17), it is easy to deduce that the aver-age number of transmissions needed by PHk successfultransmissions is 1/(1 � P). Based on this result and com-bining with Eq. (14), we propose a reliable load-awaremulticast routing path metric as follow:

FLMMRðPHkÞ ¼1Q

v j2Vk�fv ig

Pð1Þj

�Xv j0 2

Vk�fv ig

FLMMðv j0 ; SiÞ: ð18Þ

The former part on the right side of Eq. (18) can beregarded as the expected transmission counts betweenthe source node and destination node on the PHk. SoFLMMR(PHk) denotes the upper bound of additional conges-tion degree under the constraints of end-to-end reliableretransmissions for PHk. While the physical meaning ofFLMMR is obvious, we need to check if it is isotonic andmonotonic or not so that efficient multicast routing proto-cols can be designed to find minimum weight paths.

It is supposed that there are four simple paths PHa, PHb,PHc and PHd, and the relations between each of them areshown in Fig. 3. Let � be the path concatenation operationbetween paths and {�,�,�,�} be the order relation [16]. Inthe example, assuming that the weights of paths PHb andPHc satisfy: FLMMR(PHb) � FLMMR(PHc). Based on Eq. (18),it is easy to deduce that:

FLMMRðPHa � PHbÞ ¼1Q

bPð1Þj

� FLMMRðPHaÞ þ1Q

aPð1Þj

� FLMMRðPHbÞ: ð19Þ

Because the successful delivery probability of f(vj,ck(vj),Si) is below 1, therefore the formula FLMMR(PHb) �


FLMMR(PHa � PHb) and FLMMR(PHa) � FLMMR(PHa � PHb)can be established. This indicates that FLMMR is bothleft-monotonic and right-monotonic, namely FLMMR ismonotonic. However, according to Eq. (19), it is easy tosee that there is the probability of the existence ofFLMMR(PHa � PHb) � FLMMR(PHa � PHc) and FLMMR(PHb �PHd) � FLMMR(PHc � PHd). Hence, based on the definitionof isotonicity, FLMMR is not an isotonic and it cannot guar-antee that the loop-free and simple path with the lightestweight can be certainly gained in polynomial time. In orderto solve the problem of its non-isotonic property, the heu-ristic function of FLMMR is established by using the idea in[34] as follow:

FLMMRðPHkÞ Xv j0 2

Vk�fv ig

FLMM v j0 ; Si� �

� 1

Pð1Þj0

0@

1A

L

; ð20Þ

where L is a constant penalty factor. Its value range is2,3, . . ., and its value is decided by the need of target net-works. In Section 6.3, the influence that the value of Lhas on the multicast performance will be analyzed throughsimulation-based studies. From Eq. (20), it is known thatlow successful transmission probability of a MAC multicaston PHk can directly worsen the transmission cost of allMAC multicasts on this path. Therefore, the transmissioncost of single MAC multicast has a super-liner increasewith increase of transmission error probability. This rela-tion is embodied by L. This can ensure that the MAC mul-ticast with low probability of successful transmission canbe restrained from joining PHk. The unnecessary retrans-mission counts can be reduced. It tries to mitigate thedegree of network congestion caused by end-to-endretransmission and decrease the bandwidth consumptionof networks.

Compared with the conventional routing metrics, themajor advantages of FLMM and FLMMR are shown asfollows:

(1) Both of the two metrics can capture the actual avail-able bandwidth distribution, and realize the loadbalancing of network multicast flows based on local-ized degree of congestion. Although there is routeinstability problem in the load-aware routing met-rics, we can add dampening to improve route stabil-ity through choosing appropriate multicast topologyconstruction and packet forwarding schemes.

(2) FLMM and the modified FLMMR are both multicastrouting metrics with strict isotonicity and monoto-nicity. Therefore, optimal loop-free paths can begained through using these two metrics in theory.

(3) Both of the two metrics uniformly capture the intra-flow interference and inter-flow interference, andcan more effectively use the network resources com-pared with the independent manner used by MIC, etc.Besides, the interferences calculated by both of thetwo metrics are the actual transmission interferencesin unsaturated conditions. Hence, they can accuratelycapture the actual wireless channel contention.

(4) Both of the two metrics are able to take advantage ofthe WBA of wireless transmission. Additionally,

FLMMR uses the delivery ratio in MAC multicast tocalculate the path delivery ratio. It is more suitableto the multicast transmission manner comparedwith SPP [14]. Thus, more precise path delivery ratiocan be gained.

(5) Compared with FLMM, FLMMR further considers theunreliability of MAC multicast. Through calculatingeach MAC multicast delivery probability and punish-ing those MAC multicasts with low probability ofsuccessful delivery, It helps to choose the path foreach destination node to avoid the MAC multicastwith low probability of successful delivery, and alsoreduces the potential retransmission overheads.

(6) Considering the related constraints of the LPT andLPC, FLMM and FLMMR can easily realize the admis-sion control of multicast flows.

4. Multicast routing protocol for MR-MC WMNs

In this section, we incorporate our metrics and newsupport for MR-MC WMNs in MAODV to design an en-hanced MAODV-MR multicast routing protocol. LikeMAODV, MAODV-MR adopts flooding-based route discov-ery and hop-by-hop routing as its path calculation algo-rithm and packet forwarding scheme respectively. Hence,our proposed metrics can ensure that MAODV-MR cansatisfy the optimality, consistency and loop-freenessrequirements that are defined in [16]. Namely, in theory,MAODV-MR can find the multicast tree with the lightestweight in polynomial time.

MAODV-MR is a receiver-initiated multicast routingprotocol. New mesh node wishing to join the multicastgroup initiates a path finding procedure to the multicasttree such that the extra required path weight of FLMM orFLMMR is minimized. Its basic multicast tree constructionand multicast tree maintenance, including membershiprevocation, link breakage repair, group leader selectionand tree merge, etc. are similar to that of MAODV. The onlydifference is that MAODV-MR expands the protocol intoMR-MC environment, and it takes FLMM or FLMMR asthe multicast routing metric instead of HOP. Consequently,it is redesigned in the following aspects.

4.1. Localized information acquisition

It is assumed that the channel assignment is performedindependently from our proposed multicast routing proto-col. Based on the given mesh network topology, MAODV-MR expands the periodic neighbor HELLO mechanism ofMAODV and acquires the localized information on eachavailable channel through HELLO broadcast on each radio.

In order to count the link packet delivery ratios in theforward direction between adjacent nodes, any node vn

within a small interval e can randomly broadcast HELLOpackets to its neighboring nodes on every available chan-nel. It carries the HELLO packets list information fk0jng,which is actually received from each adjacent node in thelast period k � e. The current link packet delivery ratio inthe forward direction r from each adjacent node to vn canbe acquired through the ratio of k0jn and k. In order to


smooth over short-term transients in the link quality, wefurther use the ideas in [15] to cumulate the delivery ratio.Through accumulation, the link packet delivery ratio in theforward direction Pjn between any node vj and adjacentnode vn can be shown as follows:

Pjn ¼ ð1� bÞ � P0jn þ b � r; ð21Þ

where P0jn is the link packet delivery ratio of forward direc-tion in the last period and b is the weighting factor.

It is necessary that the protocol firstly acquires the cur-rent multicast traffic load distribution information in local-ized interference area on the same channel to calculated(f(vj,ck(vj),Si)) of each MAC multicast under transmissioncongestion constraints. To achieve the controllable place-ment of routers in WMNs and to reduce the complexity,we assume that MAC multicasts that are three or morehops away from each other do not interfere on the samechannel. Therefore, d(f(vj,ck(vj),Si)) can be calculated bythe available traffic load information on the one-hop andtwo-hop neighbors. The acquisition and updating of trafficload information on the adjacent nodes can be completedby piggybacking it in HELLO packets.

From the above localized metrics information acquisi-tion it is known that MAODV-MR does not use any extracontrol packets except the normal HELLO packets used byMAODV. Therefore, it will not cause extra controloverhead.

4.2. Path diversity

To achieve diversity in the paths, each intermediatenode is allowed to forward duplicate RREQs with a join flagduring predetermined period [14]. When an intermediatenode receives a new RREQ, it firstly sets an availablereceiving period a for this control packet, then updatesthe routing metrics in this control packet and constructsreverse route. If it receives duplicate RREQ, it firstly judgeswhether the current time is in the corresponding a, if so, itwill further judge whether it should update the existing re-verse route and transmit this control packet at each radioaccording to the routing metrics information as well asthe source sequence number. When each tree membernode receives new RREQ control packet, they are also re-quired to set corresponding receiving period r for the con-trol packet and to choose the reverse path with lightestweight to propagate RREP towards the request source nodeafter the expiration of the period r. When the RREP_WAIT_TIME expires, the request source node will choosethe forward route with lightest weight to send MACT con-trol packet to conduct multicast route activation accordingto each received RREP control packet. In this way thebranch of multicast tree can be set up.

From the above analysis it is easy to see that a, r andRREP_WAIT_TIME satisfy a < r < RREP_WAIT_TIME. Thevalues of the three factors are related to the concrete char-acteristics of networks and traffic distribution. The propertime value should be set when MAODV-MR is applied inpractice in order to gain optimal trade-off between pathdiversity and network control overhead.

4.3. Admission control

From the design of FLMM and FLMMR in Section 3, wecan see that the multicast traffic distribution of MR-MCWMNs is constrained by radio number, transmission qual-ity and channel congestion in the same channel. In order toimprove the practicability of MAODV-MR, the protocolsstipulate that when each node receives one RREQ controlpacket, it should not only conduct the above-mentionedoperations but also check the RREQ control packet requestaccording to Inequality (6) and (7) to determine whetheror not this request should be accepted.

5. Evaluation methodology

Using MAODV as the standard protocol, we evaluate theHOP, SPP [14], FLMM and FLMMR in NS2, especially twoperformance metrics: network throughput and packetdelivery ratio (PDR).

5.1. Simulation setup

In the simulation experiment, 49 static nodes are ran-domly placed in a 1000 300 m2 rectangle planar area.The maximal number of radios each node has is 11 andthe maximal number of available orthogonal channels is12. The network loads multiple multicast sessions. Thenumber of group nodes in each multicast session is deter-mined by the concrete simulation setup. The MAC 802.11with DCF is chosen as the MAC protocol. We implementedonly CSMA/CA without RTS, CTS or ACK for multicast MAC.The radiation track and propagation of wireless channelobeys the two-ray ground propagation model. The trans-mission power is fixed as 16 dBm, each channel capacityas 2 Mbps. The radio propagation range is fixed as 250 m.The carrier sensing range is fixed as 550 m. Concerningthe purpose of comparing the multicast routing perfor-mances, constant bit rate (CBR) traffic is used to deliverthe 512-byte packets at the rate of 10 packets/s for eachsource node. The size of the queue at every node is 50 kby-tes. The packets in a queue are scheduled on a first-in-first-out basis. The value of a, r, RREP_WAIT_TIME and b is 0.1 s,0.2 s, 0.5 s, 0.2, respectively. The experiment simulationtime is 410 s. All multicast session member nodes jointhe multicast session at the moment when the simulationstarts. Each source node delivers packets after 300 s andstops the delivery after 400 s. For each performance metric,each routing metric is stimulated on five different ran-domly generated topologies. The simulation results aregained through their average values. In addition, we as-sume that the number of radios at each node is the same.The channel assignment algorithm in our work is commonchannel approach (CCA) [7], in which all nodes are assigneda common set of channels. A summary of simulationparameters is shown in Table 2.

5.2. Performance metrics

The following metrics are used to measure the perfor-mance of the various multicast routing metrics:

Table 2Simulation parameters.

Parameter Value

Network size 49 nodes over a1000 300 m2 area

Propagation model Two-ray groundpropagation model

Transmission power 16 dBmDate transmission rate 2 MbpsMedium access control MAC802.11 with DCFPacket size (excluding header size) 512 bytesQueue size 50 kbytesQueuing policy FIFOTraffic model CBRMaximal number of radios 11Maximal number of channels 12Radio propagation range 250 mCarrier sensing range 550 mSending rate 10 packets/sa/r/RREP_WAIT_TIME/b 0.1 s/0.2 s/0.5 s/0.2Channel assignment algorithm CCADuration of each experiment 410 s of simulated timeNumber of runs per data point 5

Table 3Simulation scenarios.

Function of Parameters 49-Nodenetwork

Traffic load Number of flows From 1 to 9Number of channels 2Number of receivers of perflow

5

Penalty factor 2

Number ofchannels

Number of flows 6Number of channels From 2 to 10Number of receivers of perflow

5

Penalty factor 2


(1) Network average throughput: For multicast sessionSi, the throughput TH(Si,vj) of each destination nodevj 2 Ui is equivalent to the number of packets that vj

truly received from Si during the transmission time.The throughput TH(vj) of node vj is equivalent to theaccumulated value of each related Si correspondingto TH(Si,vj). Therefore, network throughput can bedenoted by the average value of all TH(vj).

(2) Average packet delivery ratio: For multicast sessionSi, the packet delivery ratio PDR(Si,vj) of any destina-tion node vj 2 Ui is equivalent to the ratio of thenumber of packets that vj truly received from Si dur-ing the transmission time and the number of packetsthat source node produces. Average packet deliveryratio is equivalent to the average value of packetdelivery ratio PDR(Si,vj) of all destination nodes inall multicast sessions.

6. Evaluation

The simulation results are presented in this section.Sections 6.1 and 6.2, respectively compare and analyzethe performances of all the above-mentioned routing met-rics under different traffic loads and different number ofchannels. Section 6.3 discusses the effect of penalty factorL in FLMMR.

Fig. 4. Network throughput against varying numbers of flows packed.

6.1. Function of traffic load

In this set of experiments, all network nodes areequipped with two radios and the networks have twoavailable orthogonal channels. Each time one source nodeand five destination nodes are randomly chosen to createa multicast group. In this way traffic load is gradually in-creased. Based on this network scenario, the averagethroughputs and PDRs of HOP, SPP, FLMM and FLMMR

(L = 2) under different numbers of multicast groups are

analyzed and compared. The network scenario parametersare shown in Table 3.

In order to enlarge the performance gaps between rout-ing metrics, the average throughputs of other routing met-rics are normalized based on that of HOP. The normalizedthroughputs of all routing metrics are gained as shown inFig. 4. As we can see, compared with SPP, both FLMMand FLMMR have higher throughputs with the increase oftraffic load. The traffic load is lighter when there is onlyone multicast group. In contrast with HOP, SPP can im-prove the average throughput by 29%. The averagethroughputs of FLMM and FLMMR are lower than that ofSPP (They are 10% and 25%, respectively). When the trafficload becomes heavier and there are three multicast groups,the three schemes, SPP, FLMM and FLMMR achieve about29%, 26% and 29% higher throughputs than HOP, respec-tively. When the traffic load further grows, the averagethroughput growth of SPP slows down as a whole but thatof FLMM and FLMMR grow further as a whole. When thereare 9 multicast groups and the traffic load is quite heavy,SPP, FLMM and FLMMR achieve about 8%, 57% and 64%higher throughputs than HOP, respectively.

Through the analysis for Fig. 4, it is known that whenthe traffic load is lighter, the degrees of channel congestion


created by multicast flows are smaller. The periodic controlpacket is the major factor to influence on multicast perfor-mance. Then, FLMM which is based on the channel conges-tion degree is not sensitive to the impact produced bycontrol packets. It is because that FLMM cannot directly re-flect the transmission quality of each channel. But SPP andFLMMR can choose the paths with better transmissionquality. Therefore, when the traffic load is lighter, thethroughput gained by FLMM is comparatively small amongthe three metrics. With the growth of traffic load, the inter-ferences between multicast flows increase. The channelcongestion degree becomes higher as well. At this moment,transmission interferences on various channels becomethe major factors influencing multicast performance.Among the three metrics, both FLMM and FLMMR can re-flect the practical intra-flow and inter-flow interferenceson each channel in unsaturated conditions. Therefore,when the traffic load is very heavy, the throughputs gainedby FLMM and FLMMR are both higher than that of SPP. Itindicates that under the practical high-load network sce-nario with co-existing multicast flows, when FLMM andFLMMR are used to choose paths, they are aware of the net-work real-time bandwidth distribution and reasonablyallocate the traffic flows. So they have better networkthroughput than SPP. Because FLMMR further considersthe unreliability of MAC multicast and can avoid as muchas possible the MAC multicasts with low PDR, the through-put of FLMMR is slightly higher than that of FLMM.

The average PDRs of all routing metrics under differentnumbers of multicast flows are shown in Fig. 5. It can beseen that with the increase of traffic load, the PDRs ofHOP and SPP are in faster decreasing tendency and thatof FLMM and FLMMR are in slower decreasing tendency.When the network has only one multicast group, SPP andFLMMR can both guarantee 90% and more PDRs. But FLMMcan only guarantee 83% PDR. This ratio is comparativelylower than that of SPP and FLMMR because it cannot di-rectly reflect the transmission quality. When there arethree multicast groups, the PDRs of SPP, FLMM and FLMMR

Fig. 5. Packet delivery ratio against varying number of flows packed.

are basically the same, and remain at about 78%. With theincrease of traffic load, there exist comparatively higher in-tra-flow and inter-flow interferences between networkmulticast flows. The PDR of SPP decreases because it can-not reflect this interference and cannot realize the load bal-ancing of multicast flows on various channels. But thedecreasing tendency of FLMM and FLMMR tend to be slow.It can be seen that when there are 9 multicast groups, thePDR of SPP is 22% lower than that of FLMM, and 25% lowerthan that of FLMMR. Besides, HOP tends to choose the rout-ing with shortest path and fails to consider the interferenceand channel quality. Its PDR is the lowest in any case asshown in Fig. 5. Based on above discussion, it can be seenthat FLMM and FLMMR gain better multicast performancethan that of SPP when the network is under high load. Theycan be applied to the high-load networks scenarios withpractical co-existing multicast flows.

6.2. Function of number of channels

In this set of experiments, the number of multicastgroups is fixed as 6. Each multicast group consists of onesource node and five destination nodes. Each group nodeis randomly determined. We assume that the number ofchannels is equal to the number of radio interfaces at eachnode. One more radio and channel are added each time.The number of channels is gradually increased. Based onthis scenario, the average throughputs and PDRs of HOP,SPP, FLMM and FLMMR (L = 2) under various channel num-bers are compared. The scenario parameters are shown inTable 3.

The normalized average throughput of each routingmetric under different channel numbers is shown inFig. 6. It is seen that with the increase of channel numbers,the improvement of SPP, FLMM and FLMMR show decreas-ing tendencies. Furthermore, under most circumstances,FLMM and FLMMR can gain higher throughputs than SPP.When the network channels are fewer, the interferencesbetween MAC multicasts are the major factors influencingmulticast performance. It is because that the traffic load is

Fig. 6. Network throughput against varying number of channels.


relatively heavy while the channel resources are limited. Atthis time, both FLMM and FLMMR have better networkthroughputs than SPP. This is because FLMM and FLMMR

are aware of the network real-time bandwidth distribu-tion. When the channel numbers are 2 and 3, the improve-ment of FLMM grow respectively by 13% and 10%compared with SPP. Meanwhile, the throughputs of FLMMR

grow respectively by 17% and 12% compared with SPP. Be-sides, the interferences between MAC multicasts will de-crease with the increase in channel numbers. And theperformances gaps between routing metrics can be short-ened. When the channel numbers are 9 and 10, thethroughputs of FLMMR are only 5% and 2% higher than thatof SPP. When the channel number is 10, the throughput ofFLMM is slightly lower than that of SPP.

From the above analysis, it can be seen that among theabove-mentioned four routing metrics, FLMM and FLMMR

can gain better network throughput under all scenarios.Besides, they can obviously improve the throughput thanHOP and SPP when the traffic load is relatively higherand the available channel resources are limited.

The average PDR of each routing metric under variouschannel numbers is shown in Fig. 7. It can be seen that withthe increase of channel numbers, the PDRs of four routingmetrics are in increasing tendencies. The increasing slopesof FLMM and FLMMR are lower than that of HOP and SPP. Inaddition, in most cases, FLMM and FLMMR have higherPDRs than HOP and SPP. When there are fewer channel re-sources and relatively higher traffic load, the interferenceprobability of MAC multicast is relatively higher. And nei-ther HOP nor SPP can reflect the transmission interferencesbetween MAC multicasts. So the PDRs gained by them haverelatively bigger differences compared with FLMM andFLMMR. When there are only two channels, the PDRs ofFLMM and FLMMR are 69% and 71%. But the PDRs of HOPand SPP are only 53% and 62%. With the increase of channelnumbers, the interference probability of MAC multicast de-creases. These differences will also become moderate. Itshows that when networks have 10 channels, the PDRs of

Fig. 7. Packet delivery ratio against varying number of channels.

FLMM and FLMMR are only 3% and 6% higher than that ofHOP. And the PDR of SPP is slightly higher than that ofFLMM. Compared with other routing metrics, FLMM andFLMMR can always guarantee relatively higher multicastperformance when the traffic load is relatively heavierand the channel resources are limited.

6.3. Performance influence of penalty factor on FLMMR

The purpose of introducing constant penalty factor Linto FLMMR is to prevent the MAC multicasts with lowprobability of successful packet delivery from joining mul-ticast tree. This enables FLMMR to be aware of the channelquality. In reality, the value of L directly determines theamount of MAC multicast transmission errors in pathselections. The bigger the L value is, the heavier the propor-tion becomes. Therefore, the influence of L value on net-work multicast performance needs to be analyzed. Thenetwork average throughputs and PDRs of FLMMR withvarious L values under different numbers of multicastflows are compared in this section. The simulation param-eter is set as the same as in Section 6.1.

The normalized throughputs of FLMMR with various Lvalues are shown in Fig. 8. When the number of multicastflows is below 4 and the L values are 1, 2 and 3, the net-work throughputs are the same under various numbersof flows. And they respectively increase by 25%, 26% and29% compared with HOP. When the numbers of flows are4, 5 and 6 and L value is 1, the corresponding FLMMR hasrelatively higher network throughput. When the trafficload increases and the numbers of flows are 7, 8 and 9,the corresponding FLMMR has relatively higher networkthroughput when the L value is 2, the network throughputsincrease respectively by 42%, 52% and 64% compared withHOP. But under all numbers of flows, when the L values are4 and 5, the network throughput decreases dramaticallycompared with those of other L values. The data gained un-der all scenarios are the lowest when L value is 5. Based onabove analysis, it is known that the major factor of FLMMR

to improve multicast throughput is the ratio of FLMM(vj,Si)

Fig. 8. Network throughput against varying number of flows packed.

Fig. 9. Packet delivery ratio against varying number of flows packed.


and 1=Pð1Þj0 . Proper L values can help to further improvemulticast throughput. But too much proportion can weak-en the influence of FLMM(vj,Si) part on multicast perfor-mance and decreases the improvement of multicastthroughput of FLMMR, as is the case when L values are 4and 5 in this set of experiments. Besides, the values of Lhave interrelations with network scenario factors, includ-ing multicast traffic load. Hence, when FLMMR is in practi-cal application, the L values should be set according to theconcrete target network and application requirements.

The PDRs of FLMMR with various L values are shown inFig. 9. It can be seen that with the increase of traffic load,the PDRs of FLMMR under various L values are in slowerdecreasing tendency. When the numbers of flows are 4, 5and 6 and L value is 1, the corresponding FLMMR has rela-tively higher PDRs. They are respectively 78%, 76% and 74%.When the traffic load increases and the numbers of flowsare 7, 8 and 9 and L value is 2, the corresponding FLMMR

has relatively higher PDRs. They are respectively 71%,72% and 74%. Because the relatively bigger values weakenthe influence of FLMM(vj,Si) part on multicast performance,it can be seen that the corresponding PDRs are relativelylower under all scenarios when the L values are 4 and 5.Therefore, when practical L value is set, the concrete net-work scenario and applied requirement should be consid-ered to balance the proportion of 1=Pð1Þ

j0in FLMMR. This

result is the same as stated above.

ð22Þ

7. Further discussion

In this section, the work presented in our paper is fur-ther discussed from two aspects: the joint multicast rout-ing and channel assignment problem for optimalmulticast and the practicality of routing metrics.

7.1. Cross-layer optimization

In MR-MC WMNs, channel assignment has an impact onfeasible transmission rate of a MAC multicast and the

extent to which transmissions interfere. This clearly impactsthe multicast routing used satisfy traffic demands. Con-versely, multicast routing determines the traffic flows foreach node which certainly affects channel assignment.Due to the interdependence between channel assignmentand multicast routing, it is necessary to study the cross-layer optimization of multicast routing and channel assign-ment and design dedicated channel assignment algorithmfor multicast. In Section 3, we have formulated a liner pro-gram marked LPT for solving the routing problem for opti-mal multicast throughput from bandwidth allocationaspect. We can note that all the constraints in LPT are notnecessarily sufficient for any feasible solution. Namely,LPT is not complete. Inequality (6) and (7) are both con-straints for the average flow rate in a period of the sche-dule. Obviously, they can not ensure that all active MACmulticasts in a time slot can satisfy node radio constraintsand congestion constraints in the same channel. Thus, if asolution is found that satisfies all the constraints in LPT, itmay not be a feasible solution since the channel assign-ment may not be feasible. In this paper, we are primarilyconcerned with design of high-performance multicastrouting metrics for MR-MC WMNs. In order to emphasizethe effect of proposed routing metrics on the multicast per-formance, it is assumed that the channel assignment isdone independently from our multicast optimizationframework. Therefore, the incompleteness of LPT does notaffect the design of multicast routing metrics.

If the cross-layer optimization and channel assignmentproblem are considered, the LPT needs to be added fromchannel assignment aspect.

We stipulate that each MAC multicast in the networkcan only be assigned one channel and the assignment isfixed across time slots. Due to the limit of radio number,node vi can be at most assigned with j(vi) number oforthogonal channels. Based on this constraint, it is knownthat the number of simultaneous transmissions of MACmulticasts related to a node vi cannot surpass j(vi) onany time slot s in schedule period T. Here, being relatedto vi means that vi stands for the sender or any one receiverof f(vj,ck(vj),Si). The set of MAC multicasts in the network isdefined as F. Let C = [C(f,c):1 6 f 6 jFj,1 6 c 6 jCj] denotethe F C binary channel assignment matrix correspondingto F in MR-MC WMNs, such that C(f,c) = 1 if and only ifMAC multicast f is assigned channel c. Otherwise,C(f,c) = 0. Meanwhile let K = [K(v,c):1 6 v 6 jVj,1 6 c 6jCj] denote the V C binary auxiliary matrix correspondingto V in MR-MC WMNs, such that K(v,c) = 1 if and only if atleast one MAC multicast f incident on node v has been as-signed channel c. (f 2 F(v)) Otherwise, K(v,c) = 0. Accordingto the above definitions, the node radio constraints can betransformed as: on any time slot s in schedule period T, thesum of all indicator variables X(f(vj,ck(vj),Si),s) of MACmulticasts in F(vi) is less than or equal to the sum of thevi row matrix elements in K. Its corresponding inequationis as follow:

Xf ðv j ;ckðv jÞ;SiÞ2Fðv iÞ

Xðf ðv j; ckðv jÞ; SiÞ; sÞ 6Xc2C

Kðv i; cÞ;8v i 2 V 8s:


The following constraints, meanwhile, can be derivedfrom the definitions of C and K:

Kðv j; cÞP Cðf ðv j; ckðv jÞ; SiÞ; cÞ; 8f ðv j; ckðv jÞ; SiÞ 2 Fðv jÞ;8v j 2 V ; 8c 2 C; ð23Þ

Xc2C

Kðv j; cÞ 6 jðv jÞ; 8v j 2 V ; ð24Þ

Xc2C

Cðf ðv j; ckðv jÞ; SiÞ; cÞ ¼ 1; 8f ðv j; ckðv jÞ; SiÞ 2 F: ð25Þ

Among these constraints, Inequality (24) ensures that thesum of the vi row matrix elements in K does not surpassj(vi). Inequality (25) guarantees the uniqueness of thechannel assignment.

Based on the congestion constraints in the same chan-nel, it is known that on any time slot s in period T, eachf(vj,ck(vj),Si) in the network can not be simultaneouslytransmitted with the other MAC multicasts which fall intothe adjacent interference area I(f(vj,ck(vj),Si)) and are as-signed the same channel as that of the f(vj,ck(vj),Si). Thisconstraint can be expressed as:

Xðf ðv j; ckðv jÞ; SiÞ; sÞ þXf 02

Iðf ðv j ;ckðv jÞ;SiÞÞ

Xðf 0; sÞ � Cðf 0; ckðv jÞÞ 6 1;

8f ðv j; ckðv jÞ; SiÞ 2 F; 8ckðv jÞ 2 C; 8s: ð26Þ

According to the definition of C, it is easy to derive thatInequality (26) is equivalent to Inequality (4).

We can incorporate above constraints in the LPT and ob-tain an integer liner programming denoted by ILPT to solvethe joint multicast routing and channel assignment opti-mization in concurrent multicast flow scenarios. All con-straints in ILPT are derived from both bandwidthallocation aspect and channel assignment aspect to enablethe obtained ILPT with accuracy and completeness. Thus,any solution that satisfies all constraints in ILPT will be afeasible solution. Among all constraints in ILPT, Inequality(6), (22), (23) and (24) reflect the node radio constraints.Inequality (7) and (26) describe the transmission conges-tion constraints in the same channel. Inequality (25) en-sure the uniqueness of the channel assignment. Here, theuniqueness means that each MAC multicast or radio canonly be assigned one channel. In theory, it is NP-Hard tocompute a feasible solution of ILPT because of the existenceof integer variables such as C(f,c) and K(v,c). Therefore,how to design optimal routing and channel assignmentstrategies and related approximate algorithms for multi-cast in combination with the optimization objective func-tion and feasibility constraints of ILPT is a key to makefurther improvement on the multicast throughput and net-work load capacity. It is also the focus of our furtherresearch.

7.2. Practicality of routing metrics

The main contribution of this paper is to propose twoload-aware routing metrics named FLMM and FLMMR formulticast. FLMM is inspired by the optimization objectivefunction of LPC. It is designed to aid multicast routing

protocols in computation of routes with lowest congestiondegree. FLMMR is an extension of FLMM which furtherconsiders the unreliability of MAC multicast. It is impor-tant to note that two metrics are both isotonic and mono-tonic and therefore allow efficient calculation of minimumweight and loop-free paths. That is to say, they can be ap-plied to different types of multicast routing protocols thatare widely used in wireless networks such as flooding-based route discovery and hop-by-hop routing. In the for-mula of FLMM(vj,Si), the first component represents thechannel congestion degree of related MAC multicast andthe second component reflects the wireless broadcastadvantage of wireless transmission. Thus, the physicalmeaning of the FLMM(vj,Si) is the additional average con-gestion degree of vj for multicast session Si when vj joinsrelated MAC multicast. FLMM path metric is obtained byadding up all the FLMM(vj,Si) values of individual nodesin the path. By using FLMM, each new destination nodewill select a path to the existing multicast structure suchthat the additional congestion degree required is mini-mized. This optimization objective is the same as that ofLPC, and LPC is equivalent to LPT. Therefore, FLMM can helpto balance the multicast traffic load across all availablechannels and improve multicast throughput and networkload capacity.

In this paper, we assume an ideal physical layer for net-work layer protocols and compute interference based onthe protocol interference model. In reality, an accurateacquisition of the interference information of a MAC mul-ticast f(vj,ck(vj),Si) is crucial for fully exploiting FLMM andFLMMR to increase multicast traffic carrying capacity ofMR-MC WMNs as much as possible. Due to its simplicityand to the fact that this model can be used to mimic thebehavior of IEEE 802.11 networks, the protocol interfer-ence model is suitable for our optimization framework. Itcan reduce the computational costs of the proposed met-rics and related multicast routing protocols. However, thismodel can not obtain accurate interference information ingeneral. Consequently, FLMM and FLMMR cannot be fullyaware of all the realistic interferences. In order to fully ex-ploit the potential of proposed metrics and further enhancetheir practicality, we can use physical interference modelto compute the interference instead of this model.

In the physical interference model, a packet can betransmitted successfully depending on the ratio of the re-ceived signal strength and the sum of the interferencecaused by other ongoing transmissions plus the ambientnoise. If a MAC multicast f(vj,ck(vj),Si) is active in a time slots, the transmission is successful if and only if the SINR atany receiver of f(vj,ck(vj),Si) is above a certain threshold.More formally, we have:

minu2

Nðv j ;ckðv jÞ;SiÞ

Puðv jÞNa þ

Pf ðv j0 ;ckðv jÞ;Si0 Þ2

F� f ðv j ;ckðv jÞ;SiÞf gPuðv j0 Þ � Xðf ðv j0 ; ckðv jÞ; Si0 Þ; sÞ

P SINRT ; 8s; ð27Þwhere Na is the ambient noise, Puðv jÞ is the received powerat u of the signal transmitted by node vj, and SINRT is theminimum SINR required for a successful reception that de-pends on the desired channel characteristics such as trans-mit rate.


Based on the physical interference model, it may occurthat a MAC multicast transmission is successful even ifthere is other simultaneous MAC multicast transmissionclose to it, as long as it is using a much larger transmitpower than other transmission. Thus, the conflict betweentransmissions cannot be modeled as a binary relation be-tween MAC multicasts, as it was the case with the protocolinterference model. Based on the similar concept ofweights which has been used in [30], we use a weightedconflict graph to model the physical interference betweenthe different MAC multicasts of MR-MC WMNs. The weightof a directed edge from vertex f ðv j0 ; ckðv jÞ; Si0 Þ to vertexf(vj,ck(vj),Si) is defined as:

xðf ðv j0 ; ckðv jÞ; Si0 ÞÞ ¼ maxu2

Nðv j ;ckðv jÞ;SiÞ

Pu v j0� �

Puðv jÞSINRT

� Na

;

8f v j0 ; ckðv jÞ; Si0� �

2 F � f ðv j; ckðv jÞ; SiÞ� �

: ð28Þ

Eq. (28) indicates what fraction of the maximum permissi-ble noise for f(vj,ck(vj),Si) is contributed by activity onf ðv j0 ; ckðv jÞ; Si0 Þ. Then, it is easy to know from the Inequality(27) that transmission of f(vj,ck(vj),Si) is successful in thetime slot s if and only if Inequality (29) is satisfied

Xf v j0 ;ckðv jÞ;Si0ð Þ2

F� f ðv j ;ckðv jÞ;SiÞf g

x f ðv j0 ; ckðv jÞ; Si0 Þ� �

� Xðf ðv j0 ; ckðv jÞ; Si0 Þ; sÞ

6 1; 8s: ð29Þ

Based on the Inequality (29), we can recast the congestionconstraints in the same channel as follow:

Xðf ðv j; ckðv jÞ; SiÞ; sÞ

þX

f ðv j0 ;ckðv jÞ;Si0 Þ2F� f ðv j ;ckðv jÞ;SiÞf g

xðf ðv j0 ; ckðv jÞ; Si0 ÞÞ

� Xðf ðv j0 ; ckðv jÞ; Si0 Þ; sÞ6 2; 8f ðv j; ckðv jÞ; SiÞ 2 F; 8ckðv jÞ 2 C; 8s: ð30Þ

According to Eq. (5), the Inequality (30) can also be re-laxed as:

xðSiÞR v j; ck

� �þX

f ðv j0 ;ckðv jÞ;Si0 Þ2F� f ðv j ;ckðv jÞ;SiÞf g

xðf ðv j0 ; ckðv jÞ; Si0 ÞÞ �x Si0ð Þ

Rðv j0 ; ckÞ6 2;

8f ðv j; ckðv jÞ; SiÞ 2 F; 8ckðv jÞ 2 C: ð31Þ

For the physical interference model, we use Eq. (31) asthe congestion constraints in the LPT. The LPT with physicalinterference is the same as that for protocol interferenceexcept that we replace (7) by (31). Then the channel con-gestion degree of f(vj,ck(vj),Si) can be redefined as:

dðf ðv j; ckðv jÞ; SiÞÞ ¼lðSiÞ

R v j; ck� �þ

Xf ðv j0 ;ckðv jÞ;Si0 Þ2

F� f ðv j ;ckðv jÞ;SiÞf g

xðf v j0 ; ckðv jÞ; Si0

� �Þ � lðSi0 Þ

Rðv j0 ; ckÞ: ð32Þ

FLMM and FLMMR can use Inequality (32) to computethe congestion degree d(f(vj,ck(vj),Si)) subject to the physi-

cal interference model. Obviously, a major difficulty lies inthe complexity of physical interference computing. How-ever, more accurate and realistic interference informationof a MAC multicast can be in general achieved. Then theload aware potential of FLMM and FLMMR can be fullyexploited, and their practicality can be further enhanced.Due to the complexity of handling physical interference,how to compute the accurate interference informationfor MAC multicast subject to the physical interference con-straint and demonstrate the effectiveness of our metrics inthe context of physical interference model are also inter-esting avenues of future work opened by this research.We believe that this further work could shed light on theimpact of the physical layer on optimal multicast routingdecisions.

8. Conclusions

In this paper, we addressed the design of load-awaremulticast routing metric for MR-MC WMNs. The multicastthroughput optimization problem in concurrent multicastflows scenario is first modeled and analyzed on the basisof two major constraints: the node radio constraints andthe MAC multicast congestion constraints. Our analysisindicates that the total throughput and network loadcapacity for the multiple multicast flows can be improvedthrough seeking the multicast route with lower channelcongestion degree. Based on this intuition, we proposedtwo load-aware multicast routing metrics named FLMMand FLMMR. Both metrics account for channel diversity,interference and the WBA of wireless transmission. Wealso incorporated our metrics and new support for MR-MCWMNs in MAODV to design an enhanced MAODV-MRmulticast routing protocol. FLMM aids in finding multicastroute that are better in terms of reduced intra-flow andinter-flow interference among two-hop neighbors andexploits channel diversity to improve bandwidth usageand network throughput. Compared with FLMM, FLMMR

further considers the unreliability of MAC multicast. Ourevaluation shows that the proposed metrics outperformthe SPP and HOP in terms of network throughput and pack-et delivery ratio in concurrent multicast flows scenario.FLMM and FLMMR gain better multicast performances thanSPP and HOP when the network is under high load becausethey can select the path with lowest channel congestiondegree. They can be applied to the high-loaded networkswith realistic co-existing multicast flows. Finally, we pre-sented the further work from two aspects: joint multicastrouting and channel assignment problem for optimal mul-ticast and the practicality of proposed metrics.

In future directions, we plan to research the joint mul-ticast routing and channel assignment problem for multi-cast throughput optimization and extend our cross-layeroptimization framework to handle overlapping channels.Moreover, for the case of realistic physical interference,we would like to design accurate physical interferencemeasurement method for MAC multicast by consideringphysical interference model. Finally, we also hope to inves-tigate how to design multicast routing metric to reflectnetwork rate diversity and to ensure that multicast routing


protocols make effective use of multi-rate nature of thenetwork.

Acknowledgements

The authors thank the valuable comments and sugges-tions made by the anonymous reviewers to the improve-ment of this article. This work is funded by the NationalNatural Science Foundation of China under Grant Nos.60970019 and 60773212, as well as supported by theKey Program of Hubei Provincial Natural Science Founda-tion (China) Grant No. 2009CDA132 and the FundamentalResearch Funds for the Central Universities (China) GrantNo. 2010-II-004.

References

[1] I.F. Akyildiz, X. Wang, W. Wang, Wireless mesh networks: a survey,Computer Networks 47 (4) (2005) 445–487.

[2] H. Moustafa, H. Labiod, Multicast routing in mobile ad hoc networks,Telecommunication Systems 25 (1–2) (2004) 65–88.

[3] J. Tang, G. Xue, W. Zhang, Maximum throughput and fair bandwidthallocation in multi-channel wireless mesh networks, in: Proceedingsof the IEEE Infocom’06, IEEE Inc., Piscataway, NJ, United States, 2006,pp. 1942–1951.

[4] K.N. Ramachandran, E.M. Belding, K.C. Almeroth, M.M. Buddhikot,Interference-aware channel assignment in multi-radio wirelessmesh networks, in: Proceedings of the IEEE Infocom, IEEE Inc.,Piscataway, NJ, United States, 2006, pp. 1082–1093.

[5] L. Luo, D. Raychaudhuri, H. Liu, M. Wu, D. Li, Joint association,routing and bandwidth allocation for wireless mesh networks, in:Proceedings of the 2008 IEEE Global TelecommunicationsConference, IEEE Inc., NJ, United States, 2008, pp. 600–605.

[6] E.M. Royer, C.E. Perkins, Multicast operation of the ad hoc on-demand distance vector routing protocol, in: Proceedings of theMobiCom 1999, Association for Computing Machinery, NY, UnitedStates, 1999, pp. 207–218.

[7] D.S.J. Couto, D. Aguayo, J. Bicket, R. Morris, A high-throughput pathmetric for multi-hop wireless routing, Wireless Networks 11 (4)(2005) 419–434.

[8] R. Draves, J. Padhye, B. Zill, Routing in multi-radio, multi-hopwireless mesh networks, in: Proceedings of the MobiCom 2004,Association for Computing Machinery, NY, United States, 2004, pp.114–128.

[9] Y. Yang, J. Wang, R. Kravets, Interference-aware load balancing formultihop wireless networks, Uiucdcs-r-2005-2526, University ofIllinois at Urbana-Champaign, IL, United States, 2005.

[10] A.P. Subramanian, M.M. Buddhikot, S. Miller, Interference awarerouting in multi-radio wireless mesh networks, in: Proceedings ofthe WiMESH 2006, IEEE Inc., Piscataway, NJ, United States, 2007, pp.55–63.

[11] W. Zhou, D. Zhang, D. Qiao, Comparative study of routing metric formulti-radio multi-channel wireless networks, in: Proceedings of theWCNC 2006, IEEE Inc., NY, United States, 2006, pp. 270–275.

[12] T. Liu, W. Liao, Capacity-aware routing in multi-channel multi-ratewireless mesh networks, in: Proceedings of the ICC 2006, IEEE Inc.,Piscataway, United States, 2006, pp. 1971–1976.

[13] M. Genetzakis, V.A. Siris, A contention-aware routing metric formulti-rate multi-radio mesh networks, in: Proceedings of the SECON200, IEEE Computer Society, Piscataway, NJ, United States, 2008, pp.242–250.

[14] S. Roy, D. Koutsonikolas, S. Das, Y. Hu, High-throughput multicastrouting metrics in wireless mesh networks, Ad Hoc Networks 6 (6)(2008) 878–899.

[15] X. Zhao, C.T. Chou, J. Guo, S. Jha, Probabilistically reliable on-demandmulticast in wireless mesh networks, in: Proceedings of the IEEE

WoWMoM 2008, IEEE Computer Society, Piscataway, NJ, UnitedStates, 2008, pp. 282–290.

[16] Y. Yang, J. Wang, Design guidelines for routing metrics in multihopwireless networks, in: Proceedings of the IEEE Infocom’08, IEEE Inc.,Piscataway, NJ, United States, 2008, pp. 2288–2296.

[17] P.M. Ruiz, A.F. Gomez-Skarmeta, Heuristic algorithms for minimumbandwidth consumption multicast routing in wireless meshnetworks, in: Proceedings of the ADHOC-NOW 2005, Springer-Verlag, Heidelberg, Germany, 2005, pp. 258–270.

[18] S. Murthy, A. Goswami, A. Sen, Interference-aware multicasting inwireless mesh networks, in: Proceedings of the Networking 2007,Springer-Verlag, Berlin, Germany, 2007, pp. 299–310.

[19] X. Zhao, C.T. Chou, J. Guo, S. Jha, Protecting multicast sessions inwireless mesh networks, in: Proceedings of the 31st IEEE Conferenceon Local Computer Networks, IEEE Computer Society, Los Alamitos,CA, United States, 2006, pp. 467–474.

[20] D. Koutsonikolas, Y.C. Hu, Exploring the design space of reliablemulticast protocols for wireless mesh networks, Ad Hoc Networks 7(5) (2009) 932–954.

[21] C.T. Chou, A. Misra, J. Qadir, Low-latency broadcast in multiratewireless mesh networks, IEEE Journal on Selected Areas inCommunications 24 (11) (2006) 2081–2091.

[22] J. Qadir, C.T. Chou, A. Misra, J.G. Lim, Localized minimum-latencybroadcasting in multi-rate wireless mesh networks, in: Proceedingsof the IEEE WoWMoM 2007, IEEE Computer Society, Piscataway, NJ,United States, 2007, pp. 252–259.

[23] B.H. Liu, C.T. Chou, A. Misra, S. Jha, Rate-diversity and resource-aware broadcast and multicast in multi-rate wireless meshnetworks, Mobile Networks and Applications 13 (1-2) (2008)38–53.

[24] L. Li, B. Qin, C. Zhang, H. Li, Efficient broadcasting in multi-radiomulti-channel and multi-hop wireless networks based on self-pruning, in: Proceedings of the HPCC 2007, Springer-Verlag,Heidelberg, Germany, 2007, pp. 484–495.

[25] K. Han, Y. Li, Q. Guo, M. Xiao, Broadcast routing and channelselection in multi-radio wireless mesh networks, in: Proceedings ofthe IEEE WCNC 2008, IEEE Inc., NY, United States, 2008, pp. 2188–2193.

[26] J. Qadir, A. Misra, C.T. Chou, Minimum latency broadcasting in multi-radio multi-channel multi-rate wireless meshes, in: Proceedings ofthe IEEE SECON 2006, IEEE Inc., Piscataway, NJ, United States, 2007,pp. 80–89.

[27] J. Qadir, C.T. Chou, A. Misra, J.G. Lim, Localized minimum-latencybroadcasting in multi-radio multi-rate wireless mesh networks, in:Proceedings of the IEEE WoWMoM 2008, IEEE Computer Society,Piscataway, NJ, United States, 2008, pp. 201–212.

[28] G. Zeng, B. Wang, Y. Ding, L. Xiao, M. Mutka, Efficient multicastalgorithms for multichannel wireless mesh networks, IEEETransactions on Parallel and Distributed Systems 21 (1) (2010) 86–99.

[29] F. Shahrokhi, D.W. Matula, The maximum concurrent flow problem,Journal of the Association for Computing Machinery 37 (2) (1990)318–334.

[30] K. Jain, J. Padhye, V.N. Padmanabhan, L. Qin, Impact of interferenceon multi-hop wireless network performance, in: Proceedings of theMobiCom 2003, Association for Computing Machinery, NY, UnitedStates, 2003, pp. 66–80.

[31] R. Gupta, J. Musacchio, J. Walrand, Sufficient rate constraints for qosflows in ad-hoc networks, Ad Hoc Networks 5 (4) (2007) 429–443.

[32] N. Garg, J. Konemann, Faster and simpler algorithms formulticommodity flow and other fractional packing problems, in:Proceedings of the 39th Annual Symposium on Foundations ofComputer Science, IEEE Computer Society, Washington, DC, UnitedStates, 1998, pp. 300–309.

[33] A. Sridharan, R. Guerin, C. Diot, Achieving near-optimal trafficengineering solutions for current ospf/is-is networks, IEEE/ACMTransactions on Networking 13 (2) (2005) 234–247.

[34] S. Banerjee, A. Misra, Minimum energy paths for reliablecommunication in multi-hop wireless networks, in: Proceedings ofthe MobiHoc 2002, Association for Computing Machinery, NY,United States, 2002, pp. 146–156.

tworks 55 (2011) 2150–2167 2167

Fangmin Li is now Vice Dean of InformationEngineering College of the Wuhan Univ. ofTechnology, Wuhan, Hubei, China. Hereceived his B.S. degree from the HuazhongUniv. of Science and Technology (China) andhis M.S. degree from the National Univ. ofDefense Technology (China) in 1990 and1997, respectively, both in Computer Science.In 2001, he received his Ph.D. degree at Zhe-jiang Univ. (China) in the field of ComputerScience and Engineering. In 2002, he joinedthe School of Information Engineering at the

Wuhan Univ. of Technology, where he is currently a full professor. Hismain research interests include ad hoc networks, new generation net-work architecture and embedded system design. His past research has

F. Li et al. / Computer Ne

been published in over 70 scientific journals and conference proceedingsand 16 China patents. His research has been funded by the NationalNatural Science Foundation of China and other sources. He is a seniormember of the China Computer Federation and executive member of theSensor Network Technical Committee (China).

Yilin Fang received his B.S. degree in Elec-tronic Information Engineering and M.S.degree in Communication and InformationSystem from the Wuhan Univ. of Technology,Wuhan, China, in 2004 and 2007, respectively.Since 2008, he has been a Ph.D. student ofCommunication and Information System atthe Wuhan Univ. of Technology. His recentresearch focuses on wireless mesh networks,multicast routing and cross layer optimizationin wireless networks.

Fei Hu is currently an associate professor inthe Dept. of Electrical and Computer Engi-neering at the Univ. of Alabama, Tuscaloosa,AL, USA. He received his first Ph.D. degree atShanghai Tongji Univ., China in Signal Pro-cessing (in 1999), and second Ph.D. degree atClarkson Univ. (New York State) in the field ofElectrical and Computer Engineering (in2002). He obtained his B.S. and M.S. degreesfrom the Shanghai Tiedao Univ. (China) in1993 and 1996, respectively. His researchinterests are in ad hoc sensor networks, 3G

wireless, mobile networks, wireless security and their applications in Bio-Medicine. His research has been supported by NSF, Cisco, Sprint, andother sources. He has published over 100 journal/conference papers and
book (chapters). He is a Full Sigmaxi Member, IEEE chapter officer andeditor for over five international journals.
Xinhua Liu is an adjunct professor in theSchool of Information Engineering at theWuhan Univ. of Technology, Wuhan, Hubei,China. He received his B.S. degree from theUniv. of South China (China) and his M.S.degree in Communication and InformationSystem from the Wuhan Univ. of Technologyin 1997 and 2005, respectively. Since 2005 hehas participated in several research anddevelopment projects funded by the Chinagovernment. Currently, he is pursuing hisPh.D. in the School of Information Engineer-

ing, Univ. of Technology. His research interests include wireless sensornetworks, network routing and embedded system design.

Load-aware multicast routing metrics in multi-radio multi-channel wireless mesh networks

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