traffic and interference aware scheduling for multiradio multichannel wireless mesh networks

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 2, FEBRUARY 2011 555

Traffic and Interference Aware Schedulingfor Multiradio Multichannel Wireless

Mesh NetworksNessrine Chakchouk, Student Member, IEEE, and Bechir Hamdaoui, Member, IEEE

Abstract—This paper proposes a scheduling scheme for wirelessmesh networks that are capable of multiple channel access andequipped with multiple radio interfaces. The proposed schemeis interference and traffic aware in that it increases the overallachievable throughput of the network by eliminating the inter-ference between the wireless mesh routers and maximizes thesatisfaction ratios of all active sessions by accounting for thesessions’ data rate requirements. Simulation results show thatthe proposed scheme outperforms the Tabu-based schedulingscheme and yields good tradeoffs between the achievable through-put of the network and the satisfaction ratios of the sessions.

Index Terms—Channel assignment, link scheduling, multiradio(MR) multichannel (MC) access, wireless mesh networks (WMNs).

I. INTRODUCTION

W IRELESS mesh networks (WMNs) are a new net-working paradigm that can be deployed as a wireless

backbone network [1], aiming at extending the coverage oftraditional wireless access networks via wireless multihop con-nections. In this architecture, the fixed wireless mesh routers,which form a wireless backbone, collect the traffic generatedby the client nodes and relay it to other networks, such asInternet, cellular networks, Wi-Fi, WiMAX, etc. Nowadays,due to their low cost and ease of deployment and maintenance,WMNs are appealing to several applications, such as enterprisebackbone networks, last-mile broadband Internet access, high-speed metropolitan area networks, building automation, remotemonitoring and control, etc., and hence, they are foreseeableas one of the potential networking solutions to the bandwidthscarcity problem [2]. Unlike the case of ad hoc networks,energy consumption and mobility do not usually present achallenge to WMNs. Capacity limitation, however, presents afundamental challenge to WMNs due mainly to the interferencearising from the wireless nature of the environment as well asthe scarcity of the radio/channel resources. The interference

Manuscript received May 12, 2010; revised August 8, 2010 and October 14,2010; accepted November 20, 2010. Date of publication December 23, 2010;date of current version February 18, 2011. The review of this paper wascoordinated by Prof. J. Misic.

The authors are with the School of Electrical Engineering and ComputerScience, Oregon State University, Corvallis, OR 97331-5501 USA (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2010.2102057

arising from the use of one single wireless channel in a multihopenvironment limits the number of data communications thatcan simultaneously occur in a given neighborhood, therebydecreasing the overall network throughput. One emerging so-lution to this interference problem is to enable routers withmultiradio (MR) multichannel (MC) access. For example, MCaccess can be made possible through the use of the multiplenonoverlapping channels that are provided by IEEE 802.11standards. Although the promises of MR-MC networks are ap-parent, there still requires sophisticated scheduling algorithmsthat can effectively assign these available channels and radiosto various links. In this paper, we propose a joint channel/radioassignment and time scheduling algorithm for MR-MC access-capable WMNs that improves the overall achievable networkthroughput while accounting for data traffic requirements. Theproposed scheduling scheme, which is referred to as traffic-aware interference-free scheduling (TAIFS), eliminates the in-terference among active links via a wise combination of timeand frequency domains. In addition, TAIFS exploits the channelswitching capability of the radio interfaces1 to increase channelreuse, thus improving the network capacity even further. TAIFSis also traffic aware, i.e., given a set of active paths and activelink loads, TAIFS distributes the time and channel resourcesamong the active links in a way that maximizes the capacity ofthese links with respect to their traffic loads, thus making themmeet the end-to-end bandwidth requirements as much as possi-ble and consequently enhancing the overall achievable networkthroughput. Simulation results show that TAIFS outperformsthe Tabu method [4] (a recently proposed scheduling schemealso for MR-MC networks) in terms of total achievable networkthroughput, end-to-end flow satisfactory ratio, and fairness. Theremainder of this paper is organized as follows: Section IIpresents related works. Section III describes the system model.Section IV states and formulates the studied problem. Section Vpresents the proposed scheduling scheme. Section VI evaluatesthe performance of the proposed scheme and compares it withthe Tabu-based scheduling scheme. Section VII concludes thispaper.

II. RELATED WORK

The apparent promises of MR-MC access networks have cre-ated significant research interests, resulting in numerous works

1The radio switching time is shown to be decreased to approximately 80 µsin commercial IEEE 802.11 interfaces [3].

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556 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 2, FEBRUARY 2011

ranging from performance optimization techniques to schedul-ing and channel assignment algorithms. Several studies havefocused on characterizing the achievable throughput in MR-MCnetworks [5]–[7]. In [5], Kyasanur et al. derive lower and upperbounds on the capacity of static MC networks and study theimpact of multiple radios on such network capacity. The workin [6] derives necessary and sufficient conditions for the feasi-bility of rate vectors in MR-MC WMNs and uses them to findupper bounds on the achievable throughput. In a recent work[7], Xie et al. have studied the feasibility of optimal channelassignment in MR-MC WMNs. They proved that the complex-ity of general channel assignment problems is exponential inthe number of wireless links. On the other hand, they show thatgiven a certain computing power (e.g., an off-the-shelf note-book PC), it is feasible to optimally solve channel assignmentproblems in small- and medium-scale commercial MR WMNs.There has also been several research efforts that aimed at de-veloping scheduling algorithms for MR-MC networks [4], [8]–[11]. Due to the NP-hardness of the scheduling problem, mostof these reported algorithms are heuristic schedulers. In [8],Cheng et al. study the complexity of channel scheduling underthe generalized physical interference model and under thegeneralized H-hops interference-free model and prove the suit-ability of these two models for scheduling design in MR-MCnetworks. They also provide a polynomial-time approximationinterference-free channel scheduling solution based on graphpartitioning. In [9], Ramachandran et al. introduce the MRconflict graph and a breadth-first-search-based algorithm toachieve dynamic interference-aware channel assignment. How-ever, their scheme neither completely eliminates interferencefrom the network nor does it consider traffic loads to improvethe network performances. In [10], the authors use a networkpartitioning approach for channel scheduling. They proposedan algorithm called Maxflow-based centralized channel assign-ment (MCCA) that aims at maximizing the network capacitythrough identifying the links that are most critical to carryingtraffic and then protecting them against interference. Althoughtheir approach is simple and results in polynomial-time problemformulation, it is not flexible since all the links in a partitionare fixed to a common channel, and as a consequence, itcannot achieve optimal throughput. In [4], Subramanian et al.also address the problem of assigning channels to links in MR-MC WMNs. They propose a centralized Tabu-search-basedalgorithm that assigns colors (i.e., channels) to the vertices ofthe contention graph (i.e., the links of the network graph). Theiralgorithm focuses on minimizing the network interference, andit resembles the Max-K cut problem. Although their schemesignificantly reduces the interference (closer to the lower boundon the amount of total network interference [4]), it assigns atmost one channel per active link, which results in low networkthroughput. In [11], Bahandri et al. study the performances ofa class of schedulers that uses a heuristic to make channel-to-link assignment in the presence of channels with heterogeneousrates without requiring an explicit exchange of queue/link rateinformation. This heuristic achieves some throughput gain byminimizing the incurred overhead, but it is not optimal, nor doesit outperform other scheduling heuristics that use local infor-mation exchange [12]. In this paper, we propose a scheduling

scheme that 1) eliminates the interference between wirelessrouters forming the WMN and 2) achieves a traffic-wise re-source allocation to improve the network throughput. We com-pare our proposed scheme with the Tabu search scheme [4] andshow the importance of considering data traffic rate require-ments as well as channel switching capabilities when designingscheduling algorithms. The proposed scheduling scheme usesbinary integer programming (BIP) to maximize the capacityof the active links according to their traffic loads under bothprotocol and physical interference models. It also exploits theradio-channel switching capability, which allows more spectralreuse, thus improving the achievable throughput even further.

III. NETWORK MODEL

We consider a WMN modeled as a directed graph G =(V,E), where V denotes the set of all nodes (mesh routers)in the network, and E denotes the set of physical wirelesslinks between pairs of nodes. Nodes are generated and placedrandomly in a grid to form a WMN. We assume that all thenodes transmit with a fixed power P and that there is a wirelesslink between two nodes when they are located within eachother’s transmission range. That is, for all (u, v) ∈ V 2, (u, v) ∈E when duv ≤ r, where duv is the distance between nodes uand v, and r is node u’s transmission range.

We assume that each node is equipped with m radio in-terfaces and that there is a set Ω of n orthogonal channels,each of which has a capacity b (in megabits per second). Inthis paper, we consider that all the nodes (i.e., mesh routers)are stationary and that the WMN topology is infrastructurebased with little to no topological changes. We consider a setΦ of simultaneously active sessions in the network, where eachsession si ∈ Φ is characterized by its source node sce(i), itsdestination node dest(i), its required data rate di, and the pathPi used to route session si’s traffic. Given the set of sessions(i.e., source–destination pairs, their data rates, and their paths),we extract the active subgraph G′ from the network graphG = (V,E), where G′ = (V ′, E′) is a weighted directed graphdefined as follows.

1) E ′ = {e ∈ E : ∃si ∈ Φ such that e ∈ Pi}.2) V ′ = {v ∈ V : ∃e ∈ E′ such that e is incident to v}.3) ∀e ∈ E′, the weight w(e) of link e is the sum of all the

sessions’ required data rates whose paths contain e, i.e.,

w(e) =∑

si∈Φ:Pi�e

di. (1)

The links in the active subgraph G′ are directed according tothe routing direction of active flows. It is important to mentionthat the focus of this paper is on link scheduling and chan-nel assignment algorithms rather than on routing techniques.Hence, we assume that the routers use one of the existingrouting algorithms for mesh networks (e.g., optimized link staterouting protocol (OLSR) [13], [14]) to find optimal paths for allsessions. The proposed channel assignment and link schedulingscheme assumes that all the paths are already chosen by meansof the routing algorithm.

CHAKCHOUK AND HAMDAOUI: TRAFFIC AND INTERFERENCE AWARE SCHEDULING FOR MR-MC WMNS 557

IV. PROBLEM STATEMENT AND FORMULATION

In this paper, we propose a traffic and interference-awarelink-scheduling scheme that dynamically assigns channels andtime slots among different active links while maximizing theachievable sessions’ data rates. We assume that there existsa centralized server (e.g., a designated mesh router) in thenetwork that has full knowledge of network topology, radio/channel resource availability, and active sessions’ character-istics (i.e., source/destination, required data rate, and path).Note that because, by nature of WMNs, mesh routers can besafely assumed to be stationary (i.e., network topology does notchange), and by assuming that the set of available channels andthe number of radios remain unchanged over the course of thesessions’ durations, we argue that having a centralized sched-uler/server is effective. That is, given that the topology andthe number of radios remain unchanged, the scheduler/serverwill have to periodically gather the sessions’ information, runthe proposed joint channel and time scheduling algorithm, andadvertise the scheduling solutions to all mesh routers, whichthey will then use in their communication. This schedule isupdated by the server after a certain number of time frames(adjusted according to the design goals) and transmitted again(via a common channel) to the different nodes in the network.We also assume that the schedule update period is large enoughcompared with the broadcast delay and the channel switchingdelay so that the schedule change is performed seamlesslyand that the communication between the active nodes continuesmoothly without interruption, independently of the schedulingoperations. In the remainder of this section, we will startby modeling and stating the different radio and interferenceconstraints and then define the criteria under which TAIFSperforms.

A. Radio and Interference Constraints

To carry out a direct communication, two nodes need to bewithin each other’s transmission range and have at least oneof their radio interfaces tuned to a common channel. A linke is said to be active if it has data traffic to carry, i.e., if itbelongs to at least one of the sessions’ paths. When e is active,it needs to be assigned at least one channel k. Thus, for every(e, k) ∈ E ′ × Ω, we introduce the binary variable xk

e and defineit as

xke =

{1, if link e is assigned channel k0, otherwise.

1) Interference Constraints: In this paper, we consider twointerference models: the protocol model and the cumulativemodel. In the protocol interference model, all links are assumedideal, and the interference depends only on the distances sepa-rating the nodes [4], [5], [15]. In the cumulative interferencemodel (also known as the physical interference model), theinterference depends on distances, signal-to-interference-plus-noise ratio (SINR) levels, and other channel factors that affectthe signals’ strength, such as fading and path loss [15], [16].The interference constraints under each of the two models aredescribed next.

Fig. 1. Example of network graph and its contention graph.

a) The protocol interference model: In our schedulingscheme, we are interested in maximizing the capacity of theactive links only, i.e., the links that carry traffic loads. Giventhe active subgraph G′ = (V ′, E′) defined in Section III, thecontention graph C(G′) is defined as the undirected graphwhose vertex set is E ′ (i.e., active links) and whose edge setis all pairs (u, v) ∈ E ′ × E ′ such that u interferes with v or vinterferes with u.2 Fig. 1 shows an example of a network graphand its contention graph.

In this interference model [4], [5], [15], we assume ideal linksand that the interference between nodes is mainly determinedaccording to the distance separating them. We actually considerthe following two types of interference constraints:

1) Interface-related constraints3 state that any two links thatshare at least one of their vertices cannot use the samechannel at the same time.

2) Pair-wise interference constraints state that in order for atransmission from node i to node j to be successful overthe directed link (i, j) using channel k, the following twoconditions must hold.a) dij ≤ r. That is, the receiver must be within the trans-

mitter’s transmission range.b) dlj > r for every l ∈ V ′ that is transmitting to any

h ∈ V ′ concurrently with j’s reception on the samechannel k. That is, the receiver j must be out of therange of interference caused by any other transmitter.

Therefore, by letting I ′(e) = {e′ ∈ E ′ : Transmission overe′ interferes with Reception over e}, one can write the interfer-ence constraints as

xke + xk

e′ ≤ 1 ∀ (e, e′) ∈ E ′ × I ′(e) ∀ k ∈ Ω. (2)

b) The cumulative interference model: We now formulatethe interference constraints under the cumulative model. Weconsider the Rayleigh fading channel model, which works wellin urban/no-line-of-sight environments [18]. Let us assume thata link e in the network transmits over channel k with powerP k

e . Let Ne denote the noise power measured at the receiver

2This contention graph model is similar to the one used in [17] and is usedhere to derive and formulate the different interference and radio constraints.

3These constraints are also adopted by the IEEE 802.11 standard.


of link e. We also assume that the channel gain Gee′ fromthe transmitter of link e′ to the receiver of link e depends onthe distance (between the transmitter and the receiver) and canbe written as Gee′ = K.|lee′ |−α, where α > 2 is the path lossexponent, and |lee′ | is the distance between the transmitter ofthe link e′ and the receiver of link e. A feasible schedule underthe cumulative interference model is a set of activated linkssuch that the minimum SINR requirements are satisfied. Inour case, a schedule consists of a set of links that could beactive over more than one channel at the same time. Hence, theforegoing condition should be satisfied for each link–channelpair that is active over a given time slot. To model this, we usethe activation decision variables xk

e in the SINR formula (xke :

indicates whether a link e is active over a channel k). Thus, theinterference constraints can be written as

SINR(e, k) Δ=P k

e .Gee.Fke .xk

e∑e′ �=e P k

e′ .Gee′ .F ke′ .xk

e′ + Ne> βe.x

ke (3)

where F ke represents the fading coefficient of link e and channel

k, and βe is the SINR threshold at the receiver of link e. In theRayleigh fading model, we assume that for every channel k, thefading state variables F k

e for e = 1, . . . , |E ′| are independentidentically distributed exponentially distributed random vari-ables with unit mean. We also assume that the interference fromother transmitters is much larger than the white Gaussian noiseat the receivers, and therefore, we ignore the receiver noise inour analysis. Hence, (3) becomes

SINR(e, k) Δ=P k

e .Gee.Fke .xk

e∑e′ �=e P k


e′> βe.x

ke . (4)

Note that SINR here is a random variable. Therefore, forpracticality reasons and since we do not know the fading statesahead of time (i.e., before the actual transmission occurs), (4) isreplaced by (5) (given hereafter), which uses the average valueof SINR, and is denoted by SINR and written as

SINR(e, k) =E

[P k

e .Gee.Fke .xk

e

]E

[∑e′ �=e P k


e′

] .

Hence, the interference constraints under the cumulativeinterference model are

SINR(e, k)=P k

e .Gee.xke∑

e′�=e P ke′ .Gee′ .xk

e′>β′e.x

ke ∀ e∈E ′;∀ k∈Ω.

(5)

In the particular case, where all the links use the samepower level P for transmission, the cumulative interferenceconstraints become

SINR(e, k) =Gee.x

ke∑

e′ �=e Gee′ .xke′

> β′e.xke ∀ e ∈ E ′;∀ k ∈ Ω.

(6)

2) Radio Constraints: Given that every node is equippedwith m radio interfaces, a node can at most communicate

on m different channels at a given time. By letting E ′(i) ={e ∈ E′ : e incident to i ∈ V ′}, these radio constraints can bewritten as

∑k∈Ω

∑e∈E′(i)

xke ≤ m ∀ i ∈ V ′. (7)

Similar interface constraints and interference models havealready been used in the literature [15], [16]. However, itis important to reiterate that this paper does not proposean interference model. The main contribution of this paperrather lies in the following: 1) the formulation of the schedul-ing problem in the case of a Rayleigh fading environment,2) the construction of an interference-aware frequency and timeschedule with respect to the spatial traffic distribution (Phase Iof TAIFS), and 3) the exploitation of interface switching capa-bility to increase channel reuse and further improve the networkthroughput (Phase II of TAIFS).

B. Session Satisfaction Ratio

TAIFS increases the achievable network throughput by elim-inating interference among the active links in the WMN whilesatisfying the data rate requirements of active sessions as muchas possible, i.e., while maximizing the satisfaction ratios ofactive sessions, which are defined next. Recall that a link e ∈ E′

could be used to communicate traffic belonging to multipledifferent sessions, where again, each session si is associatedwith a data rate requirement di. Hence, every link e is as-signed an aggregate data demand w(e), as defined by (1). Letw = [w(e)]e∈E′ be the vector representing all the aggregatedata demands on all active links. For all e ∈ E′, the totaldata rate that can be achieved on link e per frame (a frameis a set of time slots that repeat periodically, i.e., schedulelength) is

c(e) =

∑t=1:nts

∑k∈Ω xk,t

e

nts× b (8)

where b is the capacity of one channel, nts is the total numberof time slots per frame, and

xk,te =

{1, if link e is assigned channel k at time slot t0, otherwise.

Under the physical interference model, the link throughputc(e) can be expressed as

c(e) =

∑t=1:nts

∑k∈Ω xk,t

e .b(e, k)nts

where b(e, k) is the channel capacity given by Shannon for-mula, b(e, k) = b. log2(1 + SINR(e, k)), and SINR(e, k) isthe SINR for link e over the channel k, as defined by (3). Forevery e ∈ E′, we now define the per-session satisfaction ratiosr(e) of link e as

sr(e) =c(e)

w(e)× ns(e)


where ns(e) is the number of sessions carried out over link e,and for every session si∈Φ, the session satisfaction ratio sri is

sri = mine∈Pi

sr(e).

V. TRAFFIC-AWARE INTERFERENCE-FREE SCHEDULING

TAIFS operates in two main phases. The first phase performsa joint channel and time scheduling by solving a BIP whose ob-jective is to maximize the capacity of active links according totheir traffic loads subject to interference and radio constraints.The output of this phase is a set of active links, each assignedone time slot and a number of channels. The second phase is aheuristic that checks the possibilities of increasing the spectrumusage further by assigning more time slots and channels toactive links whenever possible (i.e., without violating radio andinterference constraints) while privileging the links with theleast satisfaction ratios.

A. TAIFS Phase I: Traffic-Aware BIP-Based Scheduling

We will start by formulating our problem of traffic andinterference-aware channel assignment as a BIP. The outcomeof this BIP is a subset of links that are assigned channels in away that they can be active at the same time without interferingwith each other. We present a BIP for each of the two studiedinterference models.

1) BIP Formulation for Channel Assignment:Case 1—Using the protocol interference model: In this

model, we assume that all the links are ideal, i.e., the proba-bility of transmission success on link e over channel k (giventhat both the radio and interference constraints are met) isPsuccess(e, k) = 1. Thus, the channel assignment program canbe formulated as

BIP(1) :

maxxk

e

∑k∈Ω

∑e∈E′

w(e)× xke

xke + xk

e′ ≤ 1 ∀ k ∈ Ω,∀ e ∈ E ′ ∀ e′ ∈ I ′(e)∑k∈Ω

∑e∈E′(i) xk

e ≤ m ∀ i ∈ V ′

xke ∈ {0, 1} ∀ k ∈ Ω ∀ e ∈ E ′.

The foregoing BIP assigns as many channels as possible toactive links while giving priority to those with higher trafficloads under interference (2) and radio (7) constraints.

Case 2—Using the cumulative interference model: Wenow consider the physical interference constraints introduced inthe previous section and account for the link reliability. In thismodel, the transmitted signals are likely to attenuate and decay,thereby increasing the chances of the receiver not being able todecode its intended signal (Psuccess(e, k) �= 1). Using (4), onecan define the transmission failure probability for a link e usingchannel k as Prob(SINR(e, k) ≤ βe.x

ke), i.e.,

Pout(e, k)

= Prob

⎛⎝P k

e GeeFke xk

e ≤ βexke

⎛⎝∑

e′ �=e

P ke′Gee′F k

e′xke′

⎞⎠

⎞⎠ .

The expression of Pout(e, k) could be derived from thefollowing result [19]:

Result : Suppose z1, z2, . . . , zn are independent exponen-tially distributed random variables with meansE[zi] = 1/λi, Then we have :

Prob

(z1 ≤

∑i=2:n

zi

)= 1− ∏

i=2:n

11+λ1/λi

Now, given that for every channel k the random variables F ke ,

e = 1, . . . , |E ′| are independent and exponentially distributedwith E[F k

e ] = 1,∀ k ∈ Ω, one can write

Pout(e, k) = 1−∏e′ �=e

1

1 +(

βe.P ke′ .Gee′ .xk

e′P k

e .Gee

) .

The probability Psuccess(e, k) of transmission success oflink e over channel k can be expressed as 1− Pout(e, k), or

Psuccess(e, k) =∏e′ �=e

1

1 +βe.P k

e′ .Gee′ .xke′

P ke .Gee

. (9)

Thus, the channel assignment per time slot optimizationproblem can be formulated as a mixed integer nonlinear pro-gram (MINLP), i.e.,

maxxk

e ,P ke

∑k∈Ω

∑e∈E′

w(e)× Psuccess(e, k)× xke

SINR(e, k) =P k

e .Gee.xke∑

e′ �=e P ke′ .Gee′ .xk

e′>β′e.x

ke ∀k∈Ω ∀e∈E ′

∑k∈Ω

∑e∈E′(i)

xke ≤ m ∀ i ∈ V ′

P ke ≤ P0 ∀ k ∈ Ω ∀e ∈ E ′

xke ∈ {0, 1} ∀ k ∈ Ω ∀e ∈ E ′.

This optimization program is equivalent to BIP(1). It aimsat maximizing the link capacity by increasing the number ofchannels assigned to each link according to its traffic demandwhile taking into account the quality of the link modeled viaPsuccess. The first set of inequalities in this program (MINLP)corresponds to the physical interference constraints. The secondset corresponds to the radio interface constraints. The third setcorresponds to the power constraints, stating that the transmis-sion power of any link must not exceed P0. Finally, the last setof inequalities corresponds to the channel-to-link assignmentindicator variable, which can only take the value of 0 or 1.This new optimization program is an MINLP, which aims atoptimizing not only the channel-to-link assignment but thetransmission power allocated for every active link–channel pair


as well. Power allocation variables appear in both expressionsof Psuccess(e, k) and SINR(e, k). When all links are assumedto transmit at the fixed power P , the probability of transmissionsuccess becomes

Psuccess(e, k) =∏e′ �=e

1

1 +βe.Gee′ .xk

e′Gee

and MINLP becomes a binary integer program termed BIP(2),i.e.,

maxxk

e

∑k∈Ω

∑e∈E′

w(e)×∏e′ �=e

1

1 +βe.Gee′ .xk

e′Gee

× xke

SINR(e, k) =Gee.x

ke∑

e′�=e Gee′ .xke′

>β′e.xke ∀k∈Ω ∀e e′ ∈E ′

∑k∈Ω

∑e∈E′(i)

xke ≤ m ∀ i ∈ V ′

xke ∈ {0, 1} ∀ k ∈ Ω ∀ e ∈ E ′.

Note that we can use the same heuristic that we de-veloped for solving the problem of joint scheduling andchannel assignment under the interference protocol model tosolve the foregoing physical interference model-based formu-lation. It suffices to solve BIP(2) in the first algorithm (thatwe will present in the next paragraph) instead of solvingBIP(1).

2) TAIFS Phase I Description: Since BIP(1) and BIP(2)perform the same task, namely channel assignment, but withrespect to two different interference models, we will use the“unique” notation BIP to refer to any of them. Because thesolutions to the BIP earlier presented may be such that someactive links may not be assigned any channels due to resource(channels and radio interfaces) limitations, we propose to itera-tively proceed to ensure that all the active links are scheduled.In the first iteration, the set of all the active links (i.e., E′) isinjected as an input to BIP [either BIP(1) or BIP(2)]. Aftersolving this BIP, there will be two disjoint sets: a set E1 of theseactive links that have been assigned channels, i.e., E1 = {e ∈E′ : ∃k ∈ Ω, xk

e = 1}, and a set E ′2 of all these unassignedactive links, i.e., E ′2 = E ′ \ E1. In the second iteration, BIP issolved again but while considering E′2 instead of E ′ as the setof active links (those active links that were not assigned anychannels during the first iteration). After solving this secondBIP, there will also be two disjoint sets: a set E2 of all activelinks that are assigned channels during the second iteration,i.e., E2 = {e ∈ E ′2 : ∃k ∈ Ω, xk

e = 1}, and a set E ′3 of all theunassigned active links, i.e., E ′3 = E ′2 \ E2. These iterationscontinue until all the active links in E′ are each assigned at leastone channel. Once this is done, each set Ei obtained duringiteration i will be assigned a time slot, during which all thelinks in Ei are scheduled to carry traffic during that time slot.These iterations constitute the first phase of TAIFS and aresummarized in Algorithm 1. In this algorithm, SM represents

a 3-D schedule matrix, containing information about the timeand channel assignment for the whole set of active links afterexecution of TAIFS Phase I.

Algorithm 1 TAIFS Phase I: BIP-Based Scheduling

1: Input: G′ = (V ′, E′), Ω, w, CM : The set of constraints.2: Output: nts: Number of time slots per time frame, SM:

Time and Channel assignment matrix.3: A← E ′

4: nts ← 05: Initialize SM to zero matrix6: while A �= ∅ do7: Solve BIP8: S ← {e ∈ A : ∃k ∈ Ω, xk

e = 1}9: A← A \ S10: Update SM and CM11: nts ← nts + 112: end while

B. TAIFS Phase II: Traffic-Aware Link-Capacity Improvement

The first algorithm described earlier partitions the set E′ ofall active links into disjoint subsets, each of which consists ofmultiple noninterfering links that can be active concurrentlyduring a time slot. Each of these links is assigned a number ofchannels that it can use during that time slot. We now propose aheuristic that aims at increasing the number of active links thatcan be scheduled during each of the time slots determined byAlgorithm 1. Basically, the heuristic tries to further increase thedata rate c(e) that every link e can achieve while prioritizing thelinks with the lowest satisfaction ratios. The heuristic works asfollows: First, it uses the outcome of Algorithm 1 (run duringTAIFS Phase I) to calculate the satisfaction ratio sr(e) of everyactive link e. Recall that the algorithm allocates one time slotand assigns a number of channels for every link e. Second, theheuristic ranks these links according to their increasing order ofsatisfaction ratios. The rationale behind this ordering is to give aprivilege to links that are farthest from satisfying their data raterequirements. Once this preparation phase is done, the heuristicpicks the “neediest” link ec among all links, and for every timeslot Tj that chronologically follows the time slot Ti that hasbeen assigned to ec in Phase I, it computes the set of channelsover which link ec could be activated during Tj without causingany interference. Among these channels, only the channelsthat, once assigned to ec, do not violate the radio constraintsare then kept. We denote this set of channels by Γ(ec, Tj). IfΓ(ec, Tj) �= ∅, then the channels from this set are assigned toec on a per channel-by-channel basis until floor(sr(ec)) = 1or until all channels in Γ(ec, Tj) are assigned to ec. The stepsneeded to perform this check operation (i.e., check whether alink ec can be activated in time slot Tj and determine the set ofchannels Γ(ec, Tj) it will use during that time slot, if possible)are given by Algorithm 2.


Algorithm 2 TAIFS PHASE II: check module

1: Input: ec: candidate link, Tj : candidate time slot, L(Tj):set of links active during Tj .

2: Output: Γ(ec, Tj): set of channels to be assigned to ec

in Tj .3: A← L(Tj), Γ(ec, Tj)← Ω, exit = 04: while (A �= ∅) and (exit = 0) do5: Pick l ∈ A6: if (ec interferes with l) or (l interferes with ec) then7: Γ(ec, Tj)← Γ(ec, Tj) \ CH(l, Tj)8: if Γ(ec, Tj) = ∅ then9: exit = 110: end if11: end if12: A← A \ {l}13: end while14: if Γ(ec, Tj) �= ∅ then15: Check channels in Γ(ec, Tj): remove those violating

radio constraints when assigned to ec during Tj

16: end if

Note that in Algorithm 2, L(Tj) (the set of links activein time slot Tj) and CH(l, Tj) (the set of channels used bylink l in time slot Tj) are deduced from the SM matrix. Afterthe check module related to the activation of link ec in slot Tj

is performed, if floor(sr(ec)) < 1, then we move to the nexttime slot Tj+1 and apply the check module for link ec andtime slot Tj+1. We keep performing the same operations untilfloor(sr(ec)) = 1 or until the end of the frame is reached, i.e.,all the time slots that follow Ti are scanned. The steps of thewhole heuristic run during TAIFS Phase II are summarized andprovided in Algorithm 3.

Algorithm 3 TAIFS Phase II: Network CapacityImprovement

1: Input: E ′sorted: Array of links in E′ sorted according totheir capacities, Tsorted: Array of time slots assigned tolinks in E ′sorted, nts, SM: The schedule matrix, sr: Thelink satisfaction ratio vector.

2: Output: SM: Time and Channel assignment matrix, sr:The link satisfaction ratio vector.

3: for counter = 1 : |E ′sorted| do4: ec ← E ′sorted[counter]5: Ti ← Tsorted[counter]6: Tj ← Ti+1

7: while (Tj ≤ nts)and(floor(sr(ec)) < 1) do8: Γ(ec, Tj)← check module(ec, Tj , L(Tj))9: if Γ(ec, Tj �= ∅) then10: Update SM11: Update (sr(ec)12: end if

13: Tj ← Tj+1

14: end while15: end for

Now that we have presented the two phases of our schemein detail, we will next show how TAIFS 1) eliminates interfer-ence between wireless routers, 2) increases spectral reuse, and3) improves network throughput.

By design, TAIFS assigns channels/time slots to active linksin such a way that they do not interfere with each other. In fact,in the first phase of our scheme, the active links are iterativelyscheduled. In each iteration, a set of links is assigned somechannels over which they can be active during a given timeslot while meeting the interference and radio constraints. Thesecond phase of our scheme conserves the “interference-free”property. Indeed, in this phase, we only activate link e in someslot Tj > Ti if and only if there exists some channel k such thatif link e transmits in slot Tj over channel k, it will not interferewith the other links that are already active in Tj , and the radioconstraint is not violated by this activation. Hence, the scheduleobtained after phase II is also interference free. However, weshould mention that in this paper, we did not consider theexternal interference originating from other wireless networkscolocated with the WMN.

On the other hand, TAIFS improves spectral reuse duringboth phases. In the first phase, spectral reuse is increased byassigning the same channel to multiple noninterfering linksthat can be active during the same time slot. Channel reuseis further increased in the second phase. In fact, note thatin the first phase, if a link e is activated in time slot Ti

(i < nts), then e is not considered for activation in time slotTj (∀ j, i + 1 ≤ j ≤ nts). In the second phase, we study thepossibility of activating link e in time slots different from thetime slot it has been initially assigned during phase I. Thus,in phase II, by increasing the number of slots in which a link isactivated, we increase not only the link capacity but the channelreuse as well (i.e., the number of users per channel at a giventime).

As far as network throughput is concerned, in our schedul-ing scheme, the channel-to-link assignment is performed withrespect to the link’s current traffic load, as shown BIP. Thus,the number of channels assigned per link is proportional tothe link’s traffic load. As a consequence, links participating inforwarding traffic of more than one session (thus representingpotential bottlenecks) are given higher priority and assignedmore channels. Hence, the per session achievable throughputwill be increased compared with the case where every link isassigned only one channel independently of the traffic load, ashas been done in previous works [9], [10], [20], [21].

In short, the proposed scheduling scheme improves thenetwork throughput and the session satisfaction ratios by1) considering the physical link reliability in a Rayleigh fadingenvironment, 2) eliminating interference among active links,3) taking into account the spatial traffic distribution during thechannel assignment process, 4) allowing the use of multiplechannels per link, and 5) privileging links with lower sessionsatisfaction ratios.


VI. PERFORMANCE EVALUATION

We now evaluate the performances of TAIFS and comparethem with those of the Tabu method [4]. We use the “sessionsatisfaction ratio” metric as a means of evaluating the effective-ness of the studied schemes, which is defined as the ratio of thesession’s achieved data rate to that of its required rate.

For completeness, we first begin by providing a briefoverview of the Tabu-based scheme. The Tabu method is acentralized channel assignment algorithm also designed forMR-MC WMNs. It consists of two main phases: In the firstphase, it assigns channels (or colors) to vertices in the con-tention graph, where each vertex corresponds to one link in theactive graph, but without taking radio interface constraints intoaccount. It starts first from a random channel assignment andthen tries to improve this assignment iteratively by using theTabu-based search technique [22]. The goal of this phase is tominimize interference by achieving a graph vertex coloring thatmaximizes the number of edges that link vertices of differentcolors in the contention graph. Since the channel assignmentobtained from the first phase may not satisfy the radio interfaceconstraints, during the second phase, the Tabu method repeat-edly applies a merge procedure to eliminate these constraintviolations.

A. Simulation Method and Setting

We implemented both TAIFS and the Tabu method inMATLAB. We used TOMLAB (linked with MATLAB) to solvethe BIPs of TAIFS Phase I. TOMLAB offers a variety of tools tosolve BIPs efficiently and reliably; the one that we used is basedon the Branch and Cut algorithm [23]. We ran our simulations,analyzed them, and plotted our results also using MATLAB.In our simulations, we generated random MR-MC WMNs,each consisting of 50 mesh routers randomly deployed in a1000 m × 1000 m area. We also fixed the transmission ranger of every node to 250 m. We consider n wireless channelsand assume that every mesh router is equipped with m radiointerfaces. For evaluation purposes, we varied n from 2 to 12and m from 2 to 6. For every generated network topology,we also generate |Φ| = 20 sessions by randomly selecting20 random pairs of source/destination nodes. MaxRate de-notes the maximum data rate that a session can require. Sessioni’s data rate, i.e., i = 1, 2, . . . , |Φ|, is set to i×MaxRate/|Φ|.The total traffic load TMaxRate is then equal to

TMaxRate =(|Φ|+ 1) MaxRate

2.

It is known that BIPs are NP-hard problems. However, thereexists some fast operation research approaches/heuristics im-plemented in Tomlab/CPLEX (e.g., Branch and Cut) that canprovide fast and accurate enough solutions to BIPs. For exam-ple, for the case of our simulations (a network with 50 nodesand 12 channels), the CPU time for computing the BIP-basedschedules is around a few milliseconds. This computation timecould further be decreased if the computation is performed bymore powerful computing machines/servers. In the followingsections, we will present the performances of our scheme interms of satisfaction ratio improvement.

Fig. 2. Impact of the number of channels and radios on the average satisfac-tion ratio for MaxRate = 10 Mb/s.

Fig. 3. Impact of the number of channels and radios on the average satisfac-tion ratio for MaxRate = 60 Mb/s.

B. Performance Behaviors

Figs. 2 and 3 show the average session satisfaction ratio whenboth the number of channels and the number of radios are var-ied, respectively, for MaxRate = 10 Mb/s and MaxRate =60 Mb/s. We can see that, for both cases of MaxRate, the av-erage session satisfaction ratio has the same trend: It increasesas the number of channels and/or radio interfaces increases. Wenotice that when the number of radios per node m is equal to 2,an increase in the number of channels has little to no impact onthe achieved per session satisfaction ratio. Likewise, when thenumber of channels n is equal to 2, an increase in the number ofradios slightly improves the average session satisfaction ratio.However, when n gets closer to 12, an increase in the number ofradios incurs a significant improvement in the achieved sessionsatisfaction ratio; this can be seen from the steep slope of theobtained curves.

On the other hand, by varying MaxRate, we can clearlysee the impact of the total traffic load on the performances.For instance, when MaxRate = 10 Mb/s, the total trafficload is T10 = 105 Mb/s, and we can achieve up to 80% persession satisfaction ratio. While when MaxRate is increased


Fig. 4. Session satisfaction ratio: MaxRate = 10 Mb/s.

Fig. 5. Session satisfaction ratio: MaxRate = 60 Mb/s.

to 60 Mb/s (i.e., total traffic load T60 = 630 Mb/s), we canonly achieve up to 15% of the required data rate. This givesus good insights on the capacity of our network during theWMN planning phase. In other words, given a set of resourcesand sessions’ rate requirements, we can determine the averagesession satisfaction ratio guaranteed by our scheduling scheme.

C. Performance Comparison

We now compare the session satisfaction ratios of TAIFSwith those of the Tabu method. Since the Tabu method doesnot completely eliminate the interference, we consider that theobtained link capacity with this scheme is c(e) = (b/|I ′(e)|+1). Hence, what we measure for the Tabu method is an upperbound rather than the actual achievable performance.

Figs. 4 and 5 show the average session satisfaction ratiosunder both schemes for two different values of MaxRate:10 and 60 Mb/s. Observe that the session satisfaction ratiorealized under our scheme is double that realized under the Tabuscheme. In addition, notice that the variation of the number

Fig. 6. Session satisfaction ratios: n = 2, and m = 6.

Fig. 7. Session satisfaction ratios: n = 6, and m = 6.

of radio interfaces affects the performances of our scheme.By looking at the satisfaction ratios depicted via the threecurves shown in Fig. 4, we can see that when n is greater thansix channels, adding two more radio interfaces increases thesatisfaction ratio level by about 20%. With the Tabu method, onthe other hand, as m increases from 4 to 6, the achieved sessionsatisfaction ratio level slightly increases and tends to stabilizearound the value of 35%.

The Tabu method performs poorly even when MaxRate isincreased to 60 Mb/s. In fact, Fig. 5 shows that when n = 6and m = 6, our scheme performs three times better than theTabu method. The figure also shows that for a given value ofMaxRate, the best session satisfaction ratio realized under ourscheme is around 15% versus 7% for the Tabu method. Wealso notice that when m = 6, with n greater than 12 channels,TAIFS achieves much better satisfaction ratio; the curve is stillfar from stabilizing at a fixed bound/value for n = 12.

Figs. 6–8 depict the satisfaction ratios of all sessions sortedin their decreasing order according to their traffic loads from


Fig. 8. Session satisfaction ratios: n = 12 and m = 6.

the session that has the highest traffic load to the session thathas the lowest traffic load when n = 2, n = 6, and n = 12,respectively. In these figures, the x-axis presents the sessionssorted from session s1 (with the highest traffic demand d1 =10 Mb/s), to session s2 (with the second highest demandd2 = 9.5 Mb/s), to session s20 (with the lowest traffic demandd20 = 0.5 Mb/s). The y-axis represents the sessions’ satisfac-tion ratios.

In our scheme, sessions with higher traffic demands (i.e.,those which have smaller indexes) are given higher prioritiesduring the channel allocation process by formulating the as-signment problem as the maximization of a weighted sum,where the weights represent the different sessions’ data raterequirements/demands. The figures clearly show that in spite ofthis predilection in resource allocation, sessions s1 to s10 havea bit lower satisfaction ratios than sessions s11 to s20. On theother hand, if we use the ratio SRi/SRj as a fairness criterion,where i ∈ [1, 10] and j ∈ [11, 20], the obtained ratios come outcloser to 1, which indicates that our scheme is also fair in termsof allocating rates among sessions. The same trend has alsobeen observed under the Tabu method. However, our schemeachieves higher session satisfaction ratios.

In essence, these obtained results show that our proposedscheme, i.e., TAIFS, outperforms the Tabu-based scheme interms of the sessions’ satisfaction ratios. Although the Tabumethod minimizes the interference in the network, it does notmake efficient use of the available resources (i.e., channelsversus time). Unlike the Tabu method, TAIFS can assign activelinks more than one channel per time slot. In addition, TAIFSallows links to switch across different channels during differenttime slots, thereby utilizing the available spectrum and radioresources more efficiently.

VII. CONCLUSION

This paper has proposed an interference-free traffic-awarescheduling scheme for MR-MC WMNs. Our scheme uses BIPto assign channels and time slots to active links while account-

ing for the sessions’ traffic loads. Results show that our schemeincreases the throughput and sessions’ satisfaction ratios by1) eliminating interference and 2) taking into account the spatialtraffic distribution. Results also show that our proposed schemeoutperforms the Tabu-based scheduling scheme in terms ofsession satisfaction ratios.

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Nessrine Chakchouk (S’10) received the NationalEngineer Diploma degree in telecommunications andthe M.S. degree with focus on networking from theHigher School of Communications of Tunis, Tunis,Tunisia, in 2008 and 2009, respectively. She is cur-rently working toward the Ph.D. degree in electricaland computer engineering with Oregon State Univer-sity, Corvallis.

Her research interests include resource manage-ment, scheduling, routing, and quality of service inwireless networks. Her current research focuses on

the optimization of resource allocation and capacity improvement of next-generation wireless networks.

Bechir Hamdaoui (M’05) received the Diploma ofGraduate Engineer degree from the National Schoolof Engineers at Tunis (BAC+6, ENIT), Tunis,Tunisia, in 1997 and the M.S. degrees in electricaland computer engineering and computer sciencesand the Ph.D. degree in computer engineering fromthe University of Wisconsin, Madison, in 2002,2004, and 2005, respectively.

From 1998 to 1999, he was a Quality Controland Planning Engineer on a power-generation plantproject under the supervision of PIRECO/FIAT Avio.

He was an Intern with Telcordia Technologies during the summer of 2004. InSeptember of 2005, he was a Postdoctoral Researcher with the Real-Time Com-puting Research Lab, University of Michigan, Ann Arbor. Since September of2007, he has been an Assistant Professor with the School of Electrical Engineer-ing and Computer Science, Oregon State University, Corvallis. He also servedas an Associate Editor for the Journal of Computer Systems, Networks, andCommunications (2007–2009). His research spans various disciplines in theareas of computer networks and wireless communications systems. His currentresearch focus is on protocol design and development, cross-layer performancemodeling and analysis, adaptive and learning techniques, quality of service(QoS) and admission control, and opportunistic resource usage and sharing.

Dr. Hamdaoui is a member of the IEEE Computer and Communications So-cieties. He is currently an Associate Editor for the IEEE TRANSACTIONS ON

VEHICULAR TECHNOLOGY (since 2009) and the Wireless Communicationsand Computing Journal (since 2009). He served as the Program Chair/Cochairof the 2009 Pervasive Wireless Networking Workshop, the 2009 WiMAX/WiBro Services and QoS Management Symposium, the 2010 Broadband Wire-less Access Symposium, and is serving for the 2011 Cooperative and CognitiveNetworks Workshop. He has also served on the program committees of severalconferences, such as the International Conference on Communications andthe International Conference on Communications and Networking. He is alsothe Student Grant and Research Competition chair for the 2011 InternationalConference on Mobile Computing and Networking.

traffic and interference aware scheduling for multiradio multichannel wireless mesh networks

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