Assigning and Scheduling Partially Overlapping Channels in Wireless Mesh Networks

Transcription

1 2013 IEEE 9th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob) Assigning and Scheduling Partially Oerlapping Channels in Wireless Mesh Networks Brigitte Jaumard and Araind Voruganti Department of Computer Science and Software Engineering Concordia Uniersity Montreal (QC) H3G 1M8, Canada Mejdi Kaddour Department of Computer Science Uniersity of Oran B.P 1524 El M Naouer, Oran 31000, Algeria Abstract The efficiency of multi-channel multi-radio wireless mesh networks can be improed with the increase of the number of channels and radios. Despite the aailability of up to 11 channels in , we can choose only up to three non oerlapping channels at any gien time. In this study, we inestigate how to design a channel assignment and a scheduling algorithm, which both exploit partially oerlapping channels in order to maximize the throughput. We next examine how much additional throughout we can obtain by doing so, in comparison with only using three orthogonal channels. Numerical experiments show that we can gain up to 25% of throughput by appropriately managing oerlapping channels. I. INTRODUCTION Wireless Mesh Networks (WMNs) [1] are currently among the most actie research areas in wireless networking due to the numerous opportunities they proide for last few miles access and the exciting challenges they set to the community at the same time. WMNs do not form a self-contained unique technology, but are made up from integrating arious existing wireless networking standards and protocols. Compared to traditional WLANs, they are empowered to offer many desirable features, such as large coerage, high network capacity, costeffectieness, scalability and resiliency. In particular, WMNs designed with multi-channel and multi-radio capabilities at mesh routers and gateways to external networks hae the potential to improe substantially the network throughput by exploiting spectrum reuse and diersity. Specifically, multiradio enables a node to communicate with more than one other node simultaneously, while multi-channel leads to higher throughput by mitigating interference. Most of WMN deices are built upon IEEE b/g, hence adopting a random access scheme at MAC layer. Besides, the multi-hop nature of WMNs requires an efficient routing protocol as in mobile ad hoc networks. But, in contrast, WMNs face less mobility and energy consumption issues. Moreoer, the traffic pattern between the nodes is relatiely stable oer a certain period of time. These obserations motiated a growing interest in adopting centralized and tightly synchronized communication schemes such as TDMA (time-diision multiple-access). In TDMA, seeral transmission links could be scheduled concurrently if mutual radio interferences do not preent the signal to be decoded with an acceptable BER (bit error rate) at each receier. In this context, the design and the optimization of WMNs need a proper handling of seeral difficult combinatorial problems. Among those, channel assignment (CA) inoles binding each radio to a channel in such a way that efficient utilization of aailable channels can be achieed while meeting traffic and connectiity requirements. Traditional CA strategies assume inherently that aailable channels are non-oerlapping (NOC). But the number of such channels is usually ery limited, e.g., IEEE b/g proides only 3 NOCs out of 11 total channels (1,6,11). Some recent studies hae shown [2], [3] that exploiting partially oerlapping channels (POC) improes spatial channel reuse and can lead to significant increase of network throughput by allowing more simultaneous transmissions. Another problem in WMNs is how to schedule transmission links, which carry downlink and uplink traffic between the mesh routers and the gateways, in a way that improes throughput, end to end delay or fairness. This problem is een harder to tackle if a physical interference model is assumed [4]. This paper introduces a comprehensie step by step approach to manage in an efficient manner the traffic and the aailable channels in multi-radio multi-channel TDMAbased WMNs. This approach relies on a set of heuristic-based algorithms which handle successiely multi-path routing, endto-end traffic estimation, channel assignment, transmission configuration generation and scheduling. A transmission configuration is defined throughout this paper as a set of nonconflicting radio links able to be scheduled inside the same TDMA slot. Different from existing work, we operate on seeral physical layer leerages, such as partially oerlapping channels and multiple data rates, while relying on an accurate SINR-based interference model. Moreoer, transmission configurations are designed to both achiee the highest possible network throughput as well as to gie more transmission opportunities to critical links adjacent to the gateways. Also, configuration scheduling is done with the aim to increase end to end throughput and fairness among the traffic flows. The remainder of this paper is organized as follows. We reiew the recent work in Section II. We discuss the interference model for multi-channel multi-radio systems in Section III. We next propose our channel assignment in Section IV and then the scheduling algorithm in SectionV that relies on a preliminary step of designing a set of transmission config /13/$ IEEE 394

2 urations. Numerical experiments are described in Section VI and conclusions are drawn in the last section. II. LITERATURE REVIEW There has been lots of work done to proe the Partially Oerlapping Channels (POC) perform better than orthogonal channels (OC) in improing the aggregated network capacity by exploiting more channels. In [5], Liu et.al. showed that POC has the potential of increasing capacity in WMNs by allowing more links to transmit simultaneously. In [6], Liu et.al. proposed a hybrid channel assignment employing POC in a distributed framework and showed that they perform better than OC, though their hybrid channel assignment strategy is not suitable for real time networks as they employ fixed and flexible radios on each node. Recently, Duarte et.al. [2] proposed a channel assignment scheme which is a deelopment of [7] proing also that the POC performs better than the OC. In [8], Feng et.al. ealuated their POCA algorithm from real testbed, their experiment results showed that the oerall network throughput of POCA is two times that of NOCA. Most of the work on the POC is to assign channels onto the links based on the distance that they are apart. If they are apart by more than the interfering range then they can be assigned with the same channel. Howeer, none of the aboe mentioned work does actually consider transmitting the end-to-end flow traffic, i.e., in [2] the nodes transmit with a probability using CSMA protocol and their work does not actually care whether the packets sent are receied instead just calculates the amount of data a node can transmit at any point of time. All of the aboe mentioned work only focused on one gateway in their simulations which is not the case in realistic networks, and they consider only one-way traffic that is either uplink or downlink for their simulations. Howeer though the logic implies the same in transmitting the traffic in either way but simulating one-way does impact on the number of radios being actie and the delay in the transmission, which are ery important to be considered for a network to be efficient. In [2], only one gateway is considered with a grid topology for their simulation, like [2], work in [9] [7] [2] [10] also considers only one gateway and all of these results only consider one way traffic. In contrast to this work we hae employed multiple gateways with random traffic in a randomly generated topology which is ery realistic and conducted simulations taking into account two way traffic. He et al. [11] proposed algorithms on how to place multiple gateways in a WMN by breaking down the gien network topology into a tree structure and restricted a node to communicate with only one gateway which is not a good approach as a node should be able to connect to more than one gateway in at least real world networks based on seeral criteria. Qin et.al. [12] consider channel switching oerhead as a measure to define the limited number of mesh nodes to be equipped with gateway functionality in WMN. Howeer none of these works did exploit the end-to-end data transmission between nodes properly. We hae deeloped seeral new strategies so that a node be able to communicate with multiple gateways but only if it meets certain criteria. Some of the existing literature [9] [12] [5] [10] put effort on scheduling end-toend data transmission in a TDMA approach by defining the transmission configurations of non-conflicting links. In our work, we hae re-defined and came up with a noel approach in defining the transmission configurations by allowing the interfering links to be part of it. III. INTERFERENCE MODEL FOR MTI-RADIO MTI-CHANEL WIRELESS SYSTEMS Most of the mesh nodes in WMN use omni-directional antennas and since they spread its spectrum all of the space, it is more likely that signals of one mesh node interfere with other node s signals resulting in loss of data due to the interference. Interference in wireless networks is an important issue to be handled carefully. The main types of interference that exists are: 1) Co-channel Interference: This could be the result if two neighbouring nodes are transmitting using the same channel and are in the interference range of each other. 2) Adjacent Channel Interference: It results if two neighbouring nodes are assigned channels that are partially oerlapping to each other. 3) Self-Interference: Eery mesh node consists of multiple radios. Self interference occurs when the radios of a node are assigned to partially oerlapped channels. A. Non-oerlapping and partially oerlapping Channels WMNs lie mostly on existing IEEE for radio and MAC layers. The popular ariants b and g operate in the ISM 2.4 GHz band and hae 13 aailable channels (only 11 channels in the US). These channels are spaced 5 MHz apart, beginning with channel 1 centered on GHz also specifies a spectral mask defining the permitted power distribution across each channel resulting in a channel width of 22 MHz for b and 20 MHz for g [13]. In both cases, three non-oerlapping channels (NOC) are aailable (1,6,11). Although considered the same in practice, NOCs are not theoretically equialent to orthogonal channels which are completely out of mutual interference. In fact, NOCs face mutual channel interference but this has little impact on transmission as signal is sufficiently attenuated. Due to the limited number of NOCs in b/g, recent studies [8], [14] indicate that utilizing partially oerlapping channels (POC) can increase network throughput dramatically. Indeed, POCs don t cause significant interference for concurrent transmission links if sufficient physical distances separate each transmitter from the receiers on other adjacent channels. Clearly, this minimum physical distance depends also on channel separation. B. Physical model Two interference models are mainly used in the literature i.e., i) the protocol interference model and ii) the physical model. Under the protocol model, a successful transmission 395

3 occurs when the intended receiing node falls inside the transmission range of its transmitting node and falls outside the interference ranges of other non-intended transmitters. On the other hand, under the physical model, a transmission is successful if and only if signal-to-interference-and-noise-ratio (SINR) at the intended receier exceeds a certain threshold so that the transmitted signal can be decoded with an acceptable bit error rate (BER). Physical model is widely considered as an accurate representation of physical layer behaior in real systems [15]. According to the physical model, a transmission l =(u, ), occurring simultaneously to a set L of other transmissions, would be successful if its associated SINR measured at the leel of the receier is greater or equal to a threshold β. It is gien by: Pd α SINR l (L) = η + u I l (l ) l L where P is the transmission power of node u, d u is the physical distance between nodes u and, α is the path loss exponent (aries usually between 2 and 6), η is the power of the ambient noise. 1. Note that all the node here are assumed to transmit with the same power leel P. I l (l ) represents the amount of interference caused by the link l =(u, ) on link l. Itisgienby: (1) I l (l )=Pd α u. (2) The aboe equations are alid when the links are on the same channel. To address the case when nodes transmit concurrently on different but POC channels, Mishra et al. [16] introduce the notion of I-factor, denoted as I f (c, c ), which measures the extent of oerlap between channels c and c. The I-factor doesn t depend on the radio propagation properties of the enironment and can be computed either analytically or empirically. It scales from 0 for completely orthogonal channels to 1 for similar channels. Table I from [16] shows the I-factor alues in IEEE b/g as a function of channel separation. So in general case where links l and l transmit on arbitrary channels c l and c l, respectiely, I l (l ) would be written as: I l (l )=Pd α u I f (c l,c l ) (3) According to [4], the relatie interference of link l on link l is the increase caused by l in the inerse of the SINR at l, namely RI l (l )= I l(l ) Pd α = I f (c l,c l ) dα u u d α. (4) u For conenience, RI l (l) is set to 0. In [17], the authors introduce the notion of the affectance of a link l, caused by a 1 We use α =4, η =10 9 mw and P =20mW set S of interfering links. It is gien by a l (S) =η l l S RI l (l ) (5) β where η l =. (6) 1 βηdα u P Intuitiely, the affectance measures at what extent some link suffers from interference while considering also its own receied power and the SINR threshold that it has to exceed. Moreoer, it has the interesting property that a set of links S is SINR-feasible (the SINR at each receiing node is at least β) iff l S, a l (S) 1. IV. CHANNEL ASSIGNMENT After setting the notations of the remainder of the paper in Section IV-A, we discuss the channel assignment in the context of a multi-channel multi-radio wireless network in Section IV-C. The proposed channel assignment algorithm relies on an estimation of the traffic on each link, which we build in Section IV-B. A. Notations We consider a wireless mesh network represented as a graph N W =(V G, L), where V is the set of mesh routers, simply referred to as nodes, G is the set of gateways, and L is the set of links. We assume that each node has n RADIO radios, and each gateway g G has ng RADIO radios. Each node or gateway can use its radios simultaneously to send or to receie data. We will use the generic index u when we do not want to distinguish the router nodes from the gateway ones. Besides, each node has a gien olume of uplink traffic to transfer to Internet through one or seeral gateways, denoted by T, and a gien olume of downlink traffic to receie from the Internet through each gateway g, denoted by Tg DL. For each link l L, we assume an uniform transmission power P. Also, we assume n C partially-oerlapping aailable channels and R possible data rates. A transmission configuration T is defined a set of transmission links L L where l L, SINR l (T \ {l}) β. Note that β denotes the SINR threshold associated with the lowest data rate in R. Communications inside the network follows a TDMA access scheme where each frame is composed from a number of fixed-duration slots. Our target is to figure out the number of slots and the mapping between each slot and a transmission configuration, in such a way that the oerall throughput is maximized. Our approach consists in soling the problem through a sequence of 4 stages, where each stage considers a different aspect and inoles a heuristic-based algorithm haing as an input the results of the preious stage and producing an output for the next stage. These stages are described in the subsequent sections. B. Stage 1: Routing and Traffic Estimation The first objectie of this stage is to select on one hand for each uplink traffic originating from a node V at set of 396

4 TABLE I I-FACTOR FOR POSSIBLE CHANNEL SEPARATIONS IN IEEE B/G Channel Separation Oerlapping Degree Algorithm 1 Estimating the Traffic to be Carried on each Link Input: N W =(V G, L),T,Tg DL Output: TRAFFIC l TRAFFIC l 0 for all l L Initialization Downlink traffic contribution to TRAFFIC l for g G and V do p g a shortest path from g to for l p g do TRAFFIC l TRAFFIC l + T DL g for g G and V do Defining the set of uplink paths p g the path in the opposite direction to p g P = {p g : g G} p the shortest path among the paths of P P {p} ; MORE p =.FALSE. if P 2 then p second shortest path of P MORE p =.TRUE. while MORE p =.TRUE. or LENGTH(p ) LENGTH(p) 0.3 do LENGTH(p) P P {p } ; p p if all paths of P hae been explored then MORE p.false. p next shortest path in P P P Uplink traffic contribution to TRAFFIC l do for each node in decreasing order of T for g G do T max g = max {TRAFFIC l + TRAFFIC l } (l,l ) p g p g:l=opp(l ) Let l(g) be such that: T max g = TRAFFIC l(g) + TRAFFIC OPP(l(g)) Call Algorithm 2 (Water Filling) on node for g G do for l p for p from to g such that T TRAFFIC l TRAFFIC l + T p p > 0 do routes (paths) to a subset of gateways, and on other hand a unique route for each downlink traffic between a gateway g and a node. On the uplink side, our intention is to associate each node only with the most closest gateways in terms of the number of hops, while ensuring a certain leel of route diersity. Indeed, the length of longer selected path between and some gateway g does not exceed the length of a shortest path between and any gateway from G by more than 30%. On the downlink side, we select the shortest path between each gateway g and node. Algorithm 2 Water-filling at node Input: T Output: T p T max if T, uplink traffic of, to be distributed oer p P, the uplink traffic amount on path p P max TRAFFIC l(g) g G ( ) T max TRAFFIC l(g) then g G Tp T max for each p P T T ( ) T max TRAFFIC l(g) Add T P g G to each path of P ITER 0 ; p shortest path of P while no more path to consider in P p the next path in P ITER ITER +1 for p P : Tp <T p do δ T p T p if ITER δ<t then Tp T p + δ ; T Tp T P contains at least 2 paths T p + T /ITER T T /ITER T or T δ =0do Afterwards, this stage estimates how much traffic will be carried on each transmission link. The complete process is described in Algorithm 1. The basic idea is to strie to distribute each uplink traffic in an een manner among the selected paths to the gateways but with minimizing at the same time the maximum amount of total traffic (uplink and downlink) that a link would carry. Algorithm 2, referred to as water-filling, gies a formal description of this. Each time an uplink traffic is distributed oer a set of paths, this algorithm fills up the least loaded paths until they carry the same traffic as the next loaded ones. The process repeats until all the paths will carry the same amount of traffic as the most loaded ones T max p. At that point, the remaining traffic is distributed eenly oer all the initially selected paths. The algorithm can stop wheneer the remaining traffic to be distributed is equal to zero. Note that the amount of traffic Tp carried on a path p is defined as the largest amount of traffic carried on an edge e on p, where e designates two links haing the same endpoints but with opposite directions. 397

5 C. Stage 2: Channel Assignment Algorithm 3 Channel Assignment C : set of aailable channels L : set of links l = argmax TRAFFIC l l L Assign channel c l =1to link l S = {l} ; L = L\{l} Initialization Main Loop: Channel Assignment to Links for each link l L in decreasing order of TRAFFIC l do c l =argmin a l ({l}) c C l S S = S {l} The way we assign channels in our Channel Assignment algorithm is as follows. Each link in the wireless radio transmission topology is assigned to the channel where it will cause the least cumulatie affectance (refer to section III-B) on the other already assigned links. This channel is picked up from a set of aailable channels ( 11) of the IEEE GHz spectrum. Also, links are processed in decreasing order of traffic, where the implied reasoning is to bring on the minimum leel of disturbance from the less loaded links on the more loaded ones and not the opposite. V. SCHEDING ALGORITHM We propose a scheduling algorithm for multi-channel multiradio wireless mesh network that relies on ordering a set of transmission configurations, where each transmission configuration is a set of links which can simultaneously transmit during a gien time slot. We first describe the design of the transmission configurations in Section V-A, and the scheduling of the configurations in order to maximize the throughput in Section V-B. A. Stage 3: Transmission Configurations A transmission configuration is a set of links which can simultaneously transmit during a gien time slot a/g Modulation and Coding Required SNR (Mbps) Scheme (db) 6 BPSK 1/ BPSK 3/ QPSK 1/ QPSK 3/ QAM 1/ QAM 3/ QAM 2/ QAM 3/ TABLE II LINK SINR PARAMETERS FOR A/G [13] According to Table II, different threshold alues apply depending on the modulation and the rate to be used. We define the transmission capacity TCAP of a configuration T as follows: TCAP(T )= RATE l. l T In order to build the configurations (see Algorithm 4), we proceed iteratiely adding one link at a time, checking each link l in turn in the decreasing order of TRAFFIC l alue. Checking includes the SINR threshold condition, and an increase alue of the transport capacity. We also make sure that each configuration contains one incoming link for each gateway in order to maximize their throughput as much as we can. When building a new configuration, we first consider the links that are not yet embedded in the preious generated configurations, and then we try to enlarge the configurations with the other links once we can add anymore such links. Procedure CHECK ADD (l, T, counter g) Adding One Yet Unconsidered Link in a Configuration under Construction Input: Transmission configuration T and link l Output: Transmission configuration T {l} if l can be added to T, T otherwise For l ω (g),g G, counter g = # of incoming links of g that belongs to T ADD. TRUE. for each endpoint u of l do MARK[u] MARK[u]+1 if MARK [u] >nu RADIO then EXIT the procedure T T {l} ; ADD.TRUE. TCAP(T ) 0 for l T do if SINR l (T \{l}) β then Compute RATE l TCAP(T ) TCAP(T )+RATE l ADD.FALSE. EXIT from the for loop if ADD =.TRUE. and TCAP(T ) > TCAP(T ) then T T {l} ; L c L c {l}; TCAP(T ) TCAP(T ) if l ω (g) for some g G then counter g counter g +1 B. Stage 4: Scheduling The scheduling step (Algorithm 5) consists of the ordering of the transmission configurations so that we maximize the throughput, without letting the packets accumulating in the buffers (i.e., minimizing the delay indirectly). In order to do so, we assume that each node, whether associated with a 398

6 Procedure ENLARGE (T ) Attempt to expand the configurations, once all links are embedded in at least one configuration for T T do for l L \ T do Let u, u V G be the two endpoints of l MARK[u] MARK[u]+1 MARK[u ] MARK[u ]+1 if MARK[u] n RADIO u T T {l } ; ADD.TRUE. ˆl l and MARK[u ] n RADIO then while ADD =.TRUE. do if SINRˆl(T \{ˆl}) <β or RATEˆl has decreased then ADD.FALSE. Select the next ˆl in T if ADD =.TRUE. then T T {l } wireless router or a gateway, has two types of buffers: the source buffers that contain the packets to be sent by that node, and the transit buffers that contain the packets on their way to their destination. Then, there is one source/buffer buffer per outgoing link, taking into account the routing defined in Section IV-B. Eery packet contains the information of source, destination and the current node. After the execution of Algorithm 1, traffic is being distributed oer all the source nodes buffers. At eery iteration we try to coer a fixed number of buffers of all the nodes which hae the highest amount of data being waiting in it and try to find a configuration which consists of at least 70% of these buffers (links). If any configuration found then schedule the transmission configuration into the time slot and if no configuration found then define a new transmission configuration which constitutes of these buffers(links). After a transmission configuration is scheduled into the time slot, then all the links that are part of the configuration pushes the packets to the other end node or to its one-hop receier in the path to the destination node. All these processes are repeated until no more packets are left in any of the outgoing buffers of any of the nodes. VI. NUMERICAL RESTS We hae conducted extensie computational experiments in order to alidate our algorithms, and then to ealuate the adantages of using oerlapping channels. We next describe, in Section VI-A, the experimental settings, as well as the parameters we hae used for the traffic and the arious algorithms. In Section VI-B, we inestigate the throughput of a multichannel multi-radio wireless mesh network with different sets of oerlapping and non oerlapping channels. We next examine the characteristics of the transmission configurations in Section VI-C, and the distribution of the channels in the channel assignment in Section VI-D. u Algorithm 4 Transmission Configurations Input: Set of links, each with an assigned channel nu RADIO : number of radios at node u Output: A set T of transmission configurations (indexed by T ) L c : set of links which are in at least one configuration L c ; c l : channel assigned to link l counter g 0 for all g G MARK[] 0 for all V ; MARK[g] 0 for all g G Step 1: Building new configurations, coering all links while L c L do Select l L \ L c such that: l =arg max TRAFFIC l l L\L c for each endpoint u of l do MARK[u] 1 T {l} ; L c L c {l} Compute SINR l and RATE l ; TCAP(T ) RATE l for l L \ L c (in decreasing order of TRAFFIC l ) do CHECK ADD (l,t, counter g) T T {T } Step 2: Including at least one incoming link for each gateway for T T and g G do Phase 1 if counter g(t )=0then for l ω (g) do CHECK ADD (l, T, counter g) If ADD =.TRUE. then go to next g for T T do Phase 2 SINR SMALL =.TRUE. while SINR SMALL =.TRUE. do for g G: counter g(t )=0do for l ω (g) do L l = {l T : SINR l (T {l}\{l }) <β} if L l = then SINR SMALL =.FALSE. ; T T {l} ˆl arg min SINR l (T {l}\{l }) l L l T T \{ˆl} ; L c L c \{ˆl} Step 3: Attempt to enlarge the configurations ENLARGE(T ) ; if L c L then Go back to Step 1 Step 4: Compute the rates of the links for T T and l T do Compute SINR l (T ) and RATE l accordingly, using Table II A. Data Instances We consider a 2-dimensional square topology with a 1km side length. We assume 4 gateways are located in position (200,800), (800, 200), (800, 800), (200, 800). We generate two sets of wireless routers, the first one according to a grid 399

7 Algorithm 5 Scheduling Input: T, L, TRAFFIC l, P, P DL,k Output: t : time slot index Bl S : buffer at node V G for the packets haing as a source to be sent on outgoing link l : buffer at node V for the packets transiting through B T l to be sent on outgoing link l : last time slot where the link l was scheduled. t LAST l eery router node (resp. gateway) is equipped with the same functionality, i.e., 2 (resp. 3) radios that are omni-directional and with constant power. Uplink and downlink traffic is randomly generated with a uniform distribution so that the alues of T and Tg are randomly generated in the interal [30, 50] Mbps. B. Throughput s. Number of Oerlapping Channels t 1 ; tl LAST 0 for each l L Distribute the source packets on each V oer the buffers Bl S according to TRAFFIC l for the uplink traffic T, where l is the first link on the route g, g G Set Bgl S DL to Tg for the downlink traffic, where l is the first link on the route g while at least one non-empty buffer Bul S or BT ul do Step 1: scheduling the packets from the sources Select the maximum number up to k of non-empty buffers from Bul S in round-robin Find a minimum set T T of configurations containing these k buffers Update the contents of the buffers Bul S and BT ul according to P, P DL, and the rates of the links used in T for T T do Assign T to time slot t t t +1 Step 2: scheduling in-transit packets Select the maximum number up to k of non-empty buffers from Bul T,u V G such that: Bul T or LENGTH(p u DST ) selected selected:b ul T is maximum, including one buffer with a minimal tl LAST Find a minimum set T T of configurations containing these k buffers Update the contents of the buffers Bul T according to Pu, Pu DL, and the rates of the links used in T for T T do Assign T to time slot t t t squares, leading then to 192 wireless routers, and then a set with a uniform random distribution of 170 routers. The transmission range of a wireless router is kept to 200m and then we make sure that each wireless router has at least one routing path toward one gateway. We use a constant power alue of 20mW for all wireless routers and gateways. In all algorithms, we use the alue of β =8.51, and the scheduling algorithm with the buffer bandwidth criterion, Performance of the arious algorithms is conducted using all 11 or a subset of the 11 channels aailable in the 2.4Ghz spectrum of the standard. For all the experiments, Fig. 1. Fig. 2. Aerage Throughput s. Channel Scenarios - Grid Topology Aerage Throughput s. Channel Scenarios - Random Topology In Figure 1 and 2, we plotted the aerage throughput of the wireless network for different channel scenarios. Channel scenario denoted by 1..x means we consider all channels between 1 and x. In the case of the grid topology (Figure 1), as soon as we use scenario 1..6, there is a throughput gain oer using only 3 orthogonal channels, with the largest gain, a 24.3 % increase of the throughput, arising when using all 11 channels. In the case of the random topology (Figure 2), the throughput gain arises as soon as we use scenario 1..7, and the largest gain corresponds to a 17.6 % increase of the throughput, when using all 11 channels. C. Characteristics of the Transmission Configurations In Figure 3, we depict a transmission configuration for one traffic instance, which is representatie of the set of generated transmission configurations. The left ertical axis corresponds to the transport capacities of the transmission configurations 400

8 (kbps), while the right ertical axis expresses the number of links in a gien configuration. The horizontal axis lists the set of transmission configurations we generated when running the algorithms for 11 channels on the grid topology for a traffic randomly generated in [30,50] Mbps. We obsere that the transport capacities ary from 279 to 180, while the number of links ary from 4 to 22. The lowest number of lists, which is rare, is explained by the selection of a central link, and the assignment of a the highest rate 54 Mbps. It then leaes little room for adding more links. Then, the throughput (not illustrated in this paper) is usually around 30% of the alue of the transport capacity alue, and is explained by the aerage length of the downlink/uplink routes, i.e., 3 hops. Fig. 3. Set of Configurations for 11 Channels - Grid Topology D. Distribution of the Channels in the Channel Assignments In Figure 4, we show the distribution of the channels in the channel assignment with 3 orthogonal channels, and then with all 11 channels in the grid topology for a traffic randomly generated in [30,50] Mbps. We obsere that the distribution is not uniform due to the criterion of the affectance for the selection of the channel to be assigned at each step of Algorithm 3. Indeed, the largest channel occurrences correspond to the channels which are the least pairwise oerlapping, while the smallest ones are associated with the most oerlapping channels. (a) Scenario 1: Channels 1, 6 and 11 Fig. 4. (b) Scenario 2: All 11 Channels Channel Distribution VII. CONCLUSION We proposed original channel assignment and scheduling algorithms in which we allow links with oerlapping channels to transmit concurrently, i.e., a scheduling algorithm which find the right compromise between a (low) interference entailed by oerlapped channels and the link rates in order to increase the throughput of a multi-channel, multi-radio system. The results show that as soon as we use 5 adjacent channels, with no pair of orthogonal channels, the resulting throughput exceeds the one reached with the use of three orthogonal channels. ACKNOWLEDGMENT B. Jaumard was supported by NSERC (Natural Sciences and Engineering Research Council of Canada) and by a Concordia Uniersity Research Chair (Tier I). REFERENCES [1] I. F. Akyildiz, X. Wang, and W. Wang, Wireless mesh networks: a surey, Computer Networks, ol. 47, no. 4, pp , [2] P. F. Duarte, Z. M. Fadlullah, K. Hashimoto, and N. 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