Multipath Selection and Channel Assignment in Wireless Mesh Networks

Transcription

1 Multipath Selection and Channel Assignent in Wireless Mesh Networs Soo-young Jang and Chae Y. Lee Dept. of Industrial and Systes Engineering, KAIST, Kusung-dong, Taejon, Korea Tel: , FAX: Eail: {pz1004, Abstract In wireless networs, it is very iportant to optiize the nuber of channels, due to the liit on the nuber of usable channels in a given networ. In addition, ultiedia services with high QoS requireents with respect to throughput and delay have recently becoe popular. To satisfy these requireents, it has becoe iportant to find a way of providing ultipath transission. A channel assignent algorith is presented that iniizes the nuber of required channels while satisfying the throughput requireents of sourcedestination pairs in ultichannel, ultiradio, ultirate wireless esh networs. A atheatical odel is proposed that considers interference effect, lin capacity, and throughput requireents. A novel channel assignent algorith is developed that taes into account ultipath selection, channel reusability, lin capacity sharing, and global optiization. The perforance of the algorith is copared with that of CPLEX, using 24 networ scenarios. The axiu gap between the CPLEX solutions and those of the proposed algorith is, on average, only 4.8%. Keywords unicast, channel assignent, ultipath transission, QoS requireent, wireless Mesh networs 1. Introduction A Wireless Mesh Networ [1, 2] is a fully connected wireless ultihop networ whose nodes are all connected to each other via ultiple hops, as shown in Figure 1. The networ is ade up of access points (APs), wireless esh routers (WMRs), and obile nodes (MNs) and supports two types of transission: (i) infrastructureless ultihop transission via counication devices, such as the widely nown Ad Hoc Networs and (ii) infrastructure-based transission via WMRs and APs. As a result, the networ can benefit, not only fro the efficiency of ultihop transissions, but also fro the stability of using APs and WMRs. APs also allow counication between wired Internet and wireless devices. To date, a nuber of notable papers on wireless esh networs have been published, on such atters as power control, channel assignent, routing echaniss, networ connectivity, and QoS issues. Aong these topics, efficient channel assignent and QoS issues are regarded as being of ajor iportance. The channel assignent proble can be seen fro two points of view. One is iniizing the nuber of required channels and the other is fully utilizing the given aount of channels. QoS issues recently have becoe the subject of particular interest, due to the increase in ultiedia streaing services such as IPTV/VOD services. Multiedia streaing services have various and high QoS requireents, according to the content or desired service qualities. The QoS requireents need to be satisfied in order to provide sealess service. Providing ultipath transission is one way of satisfying these requireents [3, 4, 6, 15, 16, 23]. Benefits of ultipath transissions are fault tolerance, load balancing, bandwidth aggregation, reduced delay, etc. [23]. Aong the, two ajor benefits of applying ultipath transission to ultiedia traffics are bandwidth aggregation and reduced delay. First, when lins suffer bad channel condition and restricted bandwidth, single path ay not satisfy the high throughput requireent of the ultiedia traffics. In such a case, ultipath transission splitting data through ultiple different paths can help to satisfy the throughput requireent. Second, when a path is broen, source-destination pair cannot counicate until the alternative path is found, which increases the end-to-end delay. However, this ultipath technique tends to increase the nuber of Figure 1 Wireless esh networs [1] 1

2 required channels in the networ. That being so, for ultipath transission, deciding the nuber of ultipaths between a source-destination pair is one of the ost iportant issues. The ter given ultipath in the paper refers to the ultipath routes fored by any existing ultipath routing algorith. Thus ultipath selection refers to the selection of a cobination of given ultipaths for flow streas. It does not ean the foration of ultipath routes as used in the other papers. The channel assignent proble of iniizing the nuber of required channels while satisfying the throughput requireents of source-destination pairs is a well-nown NP-hard proble [4]. In this paper, we present a way of solving this proble, taing into account the throughput requireents of sourcedestination pairs and other networ-related constraints in the channel assignent proble. Our solution to the proble has notable iplications. For instance, it can be applied to ultiedia services. As noted above, ultiedia services have various QoS requireents. If all the ultiedia services are being provided by the networ, it is iportant to allocate the necessary resources to each source-destination pair according to its QoS requireent, so that the networ resources can be used efficiently. For the defined proble, we propose a atheatically forulated odel using binary integer prograing and a novel channel assignent algorith. The contributions of this paper are that (i) we odel the ultipath selection and channel assignent proble atheatically, considering constraints such as lin capacity, throughput requireents, and interference effect and (ii) propose a ultipath selection and channel assignent algorith that taes ultipath selection, channel reusability, and global optiization into account. The reainder of this paper is organized as follows. Section 2 discusses related wor on channel assignent and ultipath routing. Section 3 presents the syste odel, including assuptions, interference, and networ flow odels, that is used throughout the paper. Section 4 describes the channel assignent proble in detail. Section 5 introduces the proposed channel assignent algorith. Section 6 describes the siulation and discusses the results. Section 7 concludes. 2. Related Wor 2.1. Channel Assignent Research on the channel assignent issue focuses on either distributed or centralized algoriths. In distributed algoriths, nodes use the local lin-state inforation (usually within a two-hop or three-hop range) and allocate channels in a distributed anner [7, 9, 10, 18, 20, 21]. The distributed algoriths focus ore on how to obtain -hop neighbor inforation, how to solve hidden node probles, and how to handle changes of local inforation rather than the optiization proble itself. Centralized algoriths use the global lin states and traffic inforation to centrally allocate channels to the networs [4, 5, 17, 18, 19]. Centralized algoriths are liely to yield a better solution than a distributed algorith, because they use the full networ inforation, rather than local lin-state inforation and focus ore on optiizing the networ resources and perforances. However, they require heavy overhead to aintain the networ topology and the global lin-state inforation when the networ size is big. In [4], the authors siply assign channels to lins with heavy traffic first, while in [5], an algorith to optiize throughput considering the fairness constraints is suggested. However, neither of these algoriths taes into account the networ interference. In [17], the authors consider interference between routers in the esh networs and also, the esh networ and other co-located wireless networs, while in [18], the authors try to iniize interference considering the nuber of networ interface card liitation of each node. In [19], the authors consider ulti-rate nature of the wireless networ. But none of the papers entioned above consider ultipath transission between sourcedestination pairs and lin capacity sharing aong several flows Multipath Transission and Selection The ultipath transission issue can be addressed in two ways: the ipleentation of bacup paths and concurrent paths, according to how the ultipath inforation is used. The bacup paths ethod uses ultipath inforation as a suppleent path [22]. When the current path is broen, due to obstacles or the obility of the source, destination, or relay nodes, the source-destination pair uses a suppleentary path for transission. This can reduce the end-to-end delay caused by searching for a new route while counicating. However, if the current path is sufficiently reliable and does not brea during the transission, the reserved resource in the suppleent path is wasted. The concurrent path ethod transits flows concurrently along the ultiple paths [3, 4, 6, 11]. There are two ways of ipleenting this ethod according to whether the sae flows or different flows are transitted through the ultipath. The sae flows are generally used for transissions where reliability is the critical issue, such as when sending eergency signals [11]. However, using the sae flows can generate excessive inefficiency in the networs. Different flows are ostly used to increase the throughput of the networs [3, 4, 6]. To date, ost research on the concurrent path ethod has only considered the use of the sae nuber of ultipath for all source-destination pairs in the networ. In this case, even though the QoS requireent of soe sourcedestination pairs can be achieved using only a single path, 2

3 these pairs use ore resource than a single path, which causes inefficiency in the networ. Many studies on channel assignent have dealt with throughput optiization, but few have considered the various throughput requireents of source-destination pairs. Further, to the authors nowledge, no reported study has considered a ultipath selection schee, which uses the given ultipath inforation selectively for counication in order to iniize the nuber of required channels. If the throughput requireent is high, the source-destination pair is liely to use two or ore paths for transission in order to distribute its high throughput requireent across ultiple paths. However, if the throughput requireent is low, the pair is liely to use only a single path for transission. Using the nuber of ultipath dynaically according to such deands, networ resources can be used efficiently. 3. Syste Model and Assuptions 3.1. Assuptions We assue that the ultipath inforation for each source-destination pair is given. However, a sourcedestination pair does not have to use all the given ultipath. It can selectively use a portion of the ultipath inforation, in order to iniize the nuber of required channels. A pair can flow through a ultipath siultaneously to increase the throughput of a sourcedestination pair. In this case, the su of the flow rate of its ultipaths is the flow rate of the pair. All devices, such as APs, WMRs, and MNs are equipped with several networ interface cards (NICs). There are no collisions in the networs, and the lin capacity varies according to the transission range Interference Model We define the interference set I(i, j) as the lins in the interference range of a lin (i, j), where (i, j) denotes a directional lin fro i to j. The interference effect eans that a lin (i, j) and its interference set I(i, j) cannot transit siultaneously with the sae channel. In Figure 2, the interference set I(1, 2) is the lin set {(2, 7), (3, 4)} and by the interference effect, lins (1, 2), (2, 7) and (3, 4) cannot use the sae channel. However, lins (1, 2) and (5, 6) can use the sae channel for transission Networ Flow Model The flow can be divided and flow along ultipaths siultaneously, which aes it possible to increase the throughput between the source-destination pair without using two or ore channels in one lin. By exploiting this characteristic, we can vary the ways in which the throughput requireent of the source-destination pair can be satisfied. We can use additional channels in a bottlenec lin or use additional ultipaths Routing Model We assue that when a source sends a data pacet to a destination, the entire path inforation is included in the pacet header, as is the case with the dynaic source routing (DSR) algorith [8, 11, 12]. The flow siply follows the route that the source node has decided and cannot be erged or divided at the relay nodes. 4. Proble Forulation 4.1. Notations A networ is represented by a directed graph G = (V, E), where V represent a set of vertices that includes APs, WMRs, and MNs, and E represents the transission lins. C represents the set of all the possible channels in the networ. The following notation is used in the ixed integer linear prograing (MILP) forulation: R : Throughput requireent of the sourcedestination pair C ij : Channel capacity of lin (i,j) Figure 2 Interference odel Figure 3 Saple networ for P 3

4 f ij : Data rate of the th path of the sourcedestination pair using lin (i, j) r : The end-to-end data rate of the th path of the source-destination pair (The iniu data rate aong the lins that constitute the th path of the source-destination pair is the endto-end data rate of the th path of the sourcedestination pair ) x c ij: a binary variable to represent the occupancy of channel c in a lin (i, j) w c : a binary variable to represent the occupancy of channel c in the networ P : a set of lins constituting the th path of the source-destination pair For the saple networ given in Figure 3, we have the following paths: P 11 = {(1, 3), (3, 4), (4, 5), (5, 6)} P 12 = {(1, 7), (7, 5), (5, 6)} P 21 = {(2, 4)} P 22 = {(2, 3), (3, 4)} 4.2. Objective and Constraints The objective is to iniize the nuber of required channels in the networ: Min cc w c (1) We consider the following five constraints: Throughput requireent Flow conservation equation Lin capacity Networ s channel occupancy Interference effect The first constraint is the throughput requireent. The end-to-end data rate of all source-destination pairs should be higher than their own throughput requireents. r R, for all K (2) M The second constraint is the flow conservation equation. The incoing and outgoing data rate for every node should be conserved. For each source-destination pair, the outgoing rate of the source is r, the incoing rate of the destination is r, and the difference between the incoing and outgoing rate of the relay nodes is 0. Relay nodes only relay the incoing flows to the next nodes. f ij ji { j ( i, j) P } { j ( j, i) P },,,, r if i s for all M and K r if i d for all M and K 0, otherwises, for all M and K (3) The third constraint is the lin capacity. The su of the rates of all flows that flow through a lin (i, j) should be less than the lin capacity of the lin (i, j). The capacity of a lin (i, j) is the product of the nuber of occupied channels in the lin (i, j) and the axiu transission rate of a channel, which is decided by the distance between nodes i and j. c f C x, for all ( i, j) E (4) ij ij ij K M cc The fourth constraint is the networ s channel occupancy. This constraint checs whether or not channel c is used in the networ. c c x w, for all ( i, j) E and c C (5) ij The fifth constraint is the interference effect. The sae channel cannot be used in a lin (i, j) and its interference set I(i, j). If channel c is occupied by the lin (i, j), none of the lins in the interference range of the lin (i, j) can use channel c for transission. c c xij xi j 1, for all (, i j) I(, i j), (, i j) E and cc (6) 4.3. Forulation of the Defined Multipath Selection and Channel Assignent Given the foregoing, the defined ultipath selection and channel assignent proble can be forulated as MILP1. Note that finding a channel assignent for optial perforance even when the ultiple paths are given is NP-hard [4]. This iplies that the solution tie of any nown exact algorith increases exponentially as the size of the proble increases, which eans that any nown exact algorith is inappropriate for a real-world solution to the proble. Therefore, we suggest ultipath selection and channel assignent algorith that will solve the proble and that is suitable for use in real-world applications, in a reasonable aount of tie, with satisfying results. f 4

5 MILP1: Min w subject to r R, for all K M cc ij ji { j ( i, j) P } { j ( j, i) P } 5. Algorith c r, if i s, for all M and K f f r if i d for all M and K 0, otherwises, for all M and K c f C x, for all ( i, j) E,, ij ij ij K M cc c c xij w, c c ij i j c ij c for all ( i, j) E and c C x x 1, for all ( i, j) I( i, j), ( i, j) E and c C x {0,1}, for all ( i, j) E and c C w {0,1}, for all c C The proposed algorith considers four iportant aspects to satisfy the objective of iniizing the nuber of required channels of the networs: ultipath selection, lin capacity sharing, channel reusability, and global optiization. The algorith consists of Multipath Selection, Channel Allocation and Channel Rearrangeent, as shown in Figure Multipath Selection and Channel Allocation We first assue -shortest paths are given for each source-destination pair. We then select a subset of the - shortest paths that requires least nuber of channels. The nuber of required channels for each source and destination pair is deterined by preassigning a channel in each lin with the following reuse policy. (1) Reuse the channel previously allocated to the lin by other source-destination pairs. This case is possible only when the lin has soe extra bandwidth for current source-destination pair. (2) Reuse the channel used out of its interference range of the lin The interference is not considered for initial channel assignent. However, as the iterations proceed, we tae into account the inforation about channels and data rates that were previously allocated by other flows. At each iteration, when all source-destination pairs are exained, we select the source-destination pair and its ultipaths that give the least nuber of required channels. Algorith. Multipath Selection and Channel Allocation Input: Networ graph G(V, E), Set of sourcedestination pair K, Set of subset of ultipaths of sourcedestination pair M Output: Channel allocation inforation E c, Data rate allocation inforation E d Figure 4 Channel assignent algorith Repeat For each pair K do For each subset of ultipath M do Calculate the nuber of required channels of referencing E c, E d and G(V,E). End for Select that has the least nuber of required 5

6 channels as the ultipath of the pair. End for Select the pair that has the least nuber of required channels aong set K. Allocate channels and a data rate to the ultipath of pair Update E c, E d Delete the pair fro the set K. Until set K is epty When calculating the nuber of required channels for ultipaths of a source-destination pair, we consider the inforation about previously allocated channels and data rates. This allows us to use two iportant properties: (i) lin capacity sharing by which we can reduce the nuber of required channels by using the sae lin between two or ore flows; and (ii) channel reusability, by which we can reuse the sae channel without affecting the nuber of required channels as long as we avoid the interference range of a channel. For exaple, if channel c is allocated to lin (i, j), then using channel c in the lin (i', j'), which is outside the interference range of lin (i, j), would not affect the total nuber of channels that the networ requires. In addition, using the reaining capacities of the lins to which channels and data rate were previously allocated by other flows would not affect the total nuber of channels that are required. So, in both cases, it is efficient to use channel c in the lin (i', j') and the path that contains the lins. The channel allocation process utilizes these properties. Hence, we can conclude that the channel allocation process prootes the sharing of lins or the reusing of channels, thereby reducing the total nuber of required channels Channel Rearrangeent Figure 5 Saple networ for the algorith At the start of the channel rearrangeent process, the channels are preliinarily allocated to the networ as in the previous section. Since the preliinary allocation is perfored based on each path connecting sourcedestination pair, the allocation ay inefficiently increase the nuber of required channels. To solve this proble, we reallocate channels to the lins by odifying the Welsh and Powell s algorith [13] as follows. The steps in the algorith are as follows: 1) Sort the lins in decreasing order of the size of their interference sets and initially leave every lin with no channel. 2) Traverse the lins in order, assigning channel 1 to the first lin that has not yet received an allocation, provided that it does not yet have a neighbor with channel 1 allocated to it. 3) Repeat this process with channels 2, 3, etc. until channels have been allocated to all lins. 5.3 Tie Coplexity of the Algorith Paraeters that affect the tie coplexity of the proposed algorith are the nuber of channels c, the nuber of given ultipaths, and the nuber of pairs p. Figure 6 Multipath Selection and Channel allocation (the first iteration) 6

7 Figure 7 Multipath Selection and Channel allocation (the second iteration) Figure 8 Result of channel allocation Figure 9 Channel rearrangeent 7

8 Considering basic operations of the algorith, the coplexity of the Multipath Selection and Channel Allocation is given by O(p*(p*(2 *(*(p*)*c)+2 )+p)) = O(c*p 3 * 2 *2 ) The coplexity of Channel Rearrangeent becoes O((p*) 2 +c*(p*)*(p*)) = O(c*p 2 * 2 ) Fro the above, the tie coplexity of the proposed algorith is O(c*p 3 * 2 *2 ). It shows that the coplexity depends ostly on (i) the nuber of ultipaths and (ii) the nuber of source-destination pairs Algorith Process with a Saple Networ We now exaine how the algorith wors by following an exaple given in Figure 5: 1) Overview The saple networ in Figure 5 has two sourcedestination pairs. Each pair has two given ultipaths (P1 and P2) and a throughput requireent. We can predict that the ultipath selection and channel allocation process needs two iterations to allocate channels and data rates to two source-destination pairs, one for each pair. The algorith follows the three processes: 1. Multipath Selection and Channel Allocation (the first iteration) 2. Multipath Selection and Channel Allocation (the second iteration) 3. Channel Rearrangeent 2) Process 1. Multipath Selection and Channel Allocation (the first iteration) We choose the P2 of the source-destination pair 2 that has the least nuber of required channels and allocate channels 1, 2, and 3 and a data rate 0.7 Mbps, which is the throughput requireent of source-destination pair 2. Given that there exists a source-destination pair to which channels and data rate are not assigned, continue with a second iteration. 2. Multipath Selection and Channel Allocation (the second iteration) Given that there is only one pair left, we only have to decide the route that requires the least nuber of channels. In the first iteration, channels 1, 2, and 3 are already assigned to P2 of source-destination pair 2. Considering channel reusability, using channel 1, 2, and 3 again in source-destination pair 1 does not affect the required nuber of channels. So the nuber of channels that are required for P1 and P2 of source-destination pair 1 change; the result is shown below. We select P1 of source-destination pair 1 and allocate channels 1, 2, 3, 4, and 5 and a data rate 1 Mbps, which is the throughput requireent of source-destination pair 1. Given that the channel and data rate of all pairs are allocated, we go to the channel rearrangeent process. 3. Channel Rearrangeent We delete all of the inforation about the preliinary allocation of channels, and reallocate the sallest possible channel index aong the possible channel set in order of the size of interference sets. We can see that the nuber of required channels has decreased to 4 fro 5 after channel rearrangeent. 6. Siulation The siulation is perfored using the following set up. The networ topology consists of one AP, wireless esh routers (which coprised 20% of the nodes in the networ), and obile nodes. The AP is placed in the center of the networ space. The wireless esh routers and obile nodes are distributed randoly over a terrain of 700 X 700 eters. The transission rates are given in Table 1. The axiu transission range is 90 and the interference range is 180 [5]. We use the -shortest path algorith to find the - ultipath inforation between every source-destination pair. All procedures are run on a Pentiu IV-2.8 GHz PC with 1024Mbytes of eory. In the siulation, we first copare our algorith with nearly optial solutions that are obtained by CPLEX[14] to solve the MILP forulation presented in Section 4. CPLEX is an optiization software pacage that can solve linear prograing, quadratic prograing, integer prograing, and ixed integer linear prograing probles (MILP). CPLEX applies the branch and cut technique for solving MILP probles. The nuber of branches in the branch and cut technique increases exponentially as the nuber of binary decision variables increases. Thus, we adopt a tieout stopping rule to ensure the search to terinate in a reasonable tie. For exaple, in the case of 50 nodes, 10 source-destination pairs and 2 ultipaths, the nuber of binary decision Table 1 Transission rate vs. transission range 8

9 Table 3 Throughput requireent variation test Figure 10 Nuber of nodes vs. average gap (pairs = 0.2* nodes) Figure 12 Effect of variation in throughput requireent (pairs = 0.2 * nodes) Figure 11 Nuber of nodes vs. average gap (pairs = 0.4 * nodes) variables is about 500, and it generates huge nuber of branches. Without the tieout stopping rule, the process ight continue several ore hours until the coputer runs out of eory without any progress in the solution. 10,000 seconds is a long enough CPU tie for our proble instances before the coputer runs out of eory. In ost cases, CPLEX solves channel allocation probles and yields optial solutions. However, as the probles becoe ore coplex, CPLEX fails to solve the within the tie liit of 10,000 seconds, due to the exponentially increasing nuber of branches that are generated during the search process. In this case, we copare our algorith with the best feasible solutions that CPLEX obtained within the tie liit. We test our algorith with 24 networ scenarios and copare with CPLEX solutions. Table 2 shows the siulation results. Networ scenarios are varied in ters of the nuber of nodes, the nuber of source-destination pairs, and the nuber of given ultipaths. The nubers of nodes considered are 10, 20, 30, and 50. The nuber of source-destination pairs is set at 20% and 40% of the nuber of nodes. The tests are perfored with 1, 2, and 3 ultipaths. The throughput requireents of the sourcedestination pairs have a unifor distribution between [0.5, 2.0] Mbps. For each networ scenario, five probles are randoly generated and copared with the CPLEX solutions. Figure 13 Effect of variation in throughput requireent (pairs = 0.4 * nodes) Figure 14 Effect of variation in throughput requireent (20 nodes) Figure 10 and 11 show the average gap between the algorith and CPLEX. M1, M2, and M3 indicate the nuber of given ultipaths (1, 2, and 3, respectively). In Figure 10, the nuber of source-destination pairs is 20% of the nuber of nodes, while in Figure 11 it is 40%. The outstanding perforance of the algorith can be seen fro these figures. Copared with CPLEX solutions, 9

10 Figure 15 Effect of the nuber of given ultipaths (pairs = 0.2 * nodes) Figure 16 Effect of the nuber of given ultipaths (pairs = 0.4 * nodes) when the nuber of pairs is 20% of the nuber of nodes, the axiu average gap is 4.7%, whereas when the nuber of pairs is 40% of the nuber of nodes, the worst average gap is 4.8%. Fro Figures 10 and 11, it is clear that the average gap increases as the nuber of nodes increases for singlepath cases. However, the average gap decreases as the nuber of nodes increases for two and three given ultipaths. For 30 and 50 nodes, the average gap for M1 is saller than that for M2 and M3 in Figure 10, whereas in Figure 11 the average gap for M1 is greater than that for M2 and M3. The reason for these results is the relationship between the coplexity of the probles and the solutions yielded by CPLEX. CPLEX ostly fails to yield an optial solution within the tie liit when the proble becoes coplex. Next, we test the algorith by varying the siulation environent with respect to throughput requireent and the nuber of given ultipaths between sourcedestination pairs. To deterine the effect of variation in throughput requireent, we eep other siulation paraeters constant and vary the throughput requireents of source-destination pairs aong 0.5, 1, and 2 Mbps. To deterine the effect of the nuber of given ultipaths, we eep other siulation paraeters constant and vary the nuber of given ultipath of source-destination pairs aong 1, 2, and 3. Figures 12, 13, and 14 represent the effect of different throughput requireents on the nuber of channels for different nubers of nodes and pairs, while eeping other paraeters fixed. Table 3 shows the test conditions of Figures 12, 13 and 14. For exaple, in Figure 12, the throughput requireent is varied fro 0.5 Mbps to 2 Mbps and the nuber of nodes is varied fro 10 to 50, while the ratio of the nuber of pairs to the nuber of nodes is fixed at 1:5. Fro Figures 12, 13, and 14, we can see that the nuber of channels increases only slightly as the throughput, nuber of nodes, and nuber of pairs increase. This is because our algorith eploys lin sharing and channel reuse. The flows in the networ tend to share or reuse the sae channel frequently, in order to reduce the total usage of channels in the networ. Figures 15 and 16 show the effect of the nuber of given ultipaths on the nuber of channels. In Figure 15, the nuber of given ultipaths varies fro 1 to 3, the nuber of nodes varies fro 10 to 50, and the ratio of the nuber of pairs to the nuber of nodes is 1:5. In Figure 16, the nuber of given ultipaths varies fro 1 to 3, the nuber of nodes varies fro 10 to 30, and the ratio of the nuber of pairs to the nuber of nodes is 2:5. Figure 17 Tie coplexity of the algorith (tie vs. pairs) 10

11 Fro Figures 15 and 16, we can see that the nuber of channels decreases as the nuber of given ultipaths increases. The networ scenarios with three given ultipaths provide ore opportunity to choose routes that utilize lin sharing and channel reusability than those with only one or two given ultipaths. Note that we do not have to provide flows to all the given ultipaths. Figure 17 shows the tie coplexity of the algorith for axiu 100 nodes. 20% and 40% of the node size are considered for the nuber of source-destination pairs with two given ultipaths. Fro the figure, it is clear that the suggested algorith is powerful to provide practical solution to the ultipath selection and channel assignent in wireless esh networs. 7. Conclusion We have addressed the channel assignent proble of iniizing the nuber of channels while considering the throughput requireents of source-destination pairs in ultichannel, ultiradio, ultirate wireless esh networs. We forulated the channel assignent proble, which is a well-nown NP-hard proble, through binary integer prograing and proposed a novel algorith for assigning channels. Specifically, the atheatical odel considers such constraints as interference effect, lin capacity, and throughput requireents and the algorith taes two processes into account to obtain better solutions. First, we suggested a pair selection process. When selecting a pair to allocate next, we refer to the previously allocated channel and data rate inforation to exploit the benefits of channel reusability and lin capacity sharing. Second, we suggested a channel rearrangeent process. The allocation of one pair at a tie iteratively ay cause the solution to fall into a local optiu. Hence, in this process, we delete the previously allocated channel inforation and reallocate channels to the networs. Fro the analyses, it is evident that the nuber of channels decreases as the nuber of given ultipaths increases and slowly increases as the throughput requireents of source-destination pairs increase. This is due to the factors that our algorith considers. A greater nuber of given ultipaths offers ore opportunity to exploit the benefits of channel reusability and the sharing of lin capacity. In addition, sharing lin capacity alleviates the increent of throughput requireents of source-destination pairs. The perforance of the proposed algorith was evaluated by running siulations of 24 different sets of networ scenarios and coparing the results to the CPLEX solutions, which give nearly optial values. CPLEX tends to fail to obtain optial solutions when the proble sizes get bigger and, as a result, becoe coplex. In these cases, we copared our results with the solutions that CPLEX obtained during 10,000 seconds. The siulation results verify that the proposed channel assignent algorith is very effective. References 1. Ayildiz, I.F., Wang, X., and Wang, W., (2005). Wireless esh networs: a survey. Coputer Networs Journal (Elsevier). 2. Bruno, R., Conti, M., and Gregori, E., (2005) Mesh networs: coodity ultihop ad hoc networs. IEEE Counications Magazine, v.43(3), pp Sheriff, I., and Belding-Royer, E., (2006). Multipath Selection in Multi-radio Mesh Networs. Broadnets 2006, pp Raniwala, A., Gopalan, K., and Chiueh, T.-C., (2004). Centralized channel assignent and routing algoriths for ulti-channel wireless esh networs. ACM Mobile Coputing and Counications Review (MC2R), vol 8(2), pp Alicherry, M., Bhatia, R., and Li, L., (2006). Joint Channel Assignent and Routing for Throughput Optiization in Multiradio Wireless Mesh Networs. IEEE Journal on Selected Areas in Counications, Vol. 24, No. 11, pp Tsai, J.W., and Moors, T., (2007). Interference-aware Multipath Selection for Reliable Routing in Wireless Mesh Networs. Mobile Adhoc and Sensor Systes, pp Raniwala, A., and Chiueh, T., (2005). Architecture and algoriths for an IEEE based ultichannel wireless esh networ. INFOCOM 2005, Vol. 3, pp Johnson, D.B., and Maltz, D.A., (1996). Dynaic source routing in ad hoc networs. Mobile Coputing, Vol Cidon, I., and Sidi, M., (1989). Distributed assignent algoriths for ultihop pacet radio networs. IEEE Transactions on Coputers, vol.38, no.10, pp Ko, B.-J., Misra, V., Padhye, J., and Rubenstein, D., (2007). Distributed channel assignent in ulti-radio esh networs. IEEE Wireless Counications and Networing Conference, pp Leung, R., Liu, J., Poon, E., Chan, A.L.C., and Li, B., (2001). MP-DSR: a QoS-aware ulti-path dynaic source routing protocol for wireless ad-hoc networs. Proceedings of the 26th IEEE Annual Conference on Local Coputer Networs, pp Johnson, D.B., Maltz, D.A., and Broch, J., (2001). DSR: the dynaic source routing protocol for ultihop wireless ad hoc networs. Ad hoc networing, pp Welsh, D.J.A., and Powell, M.B., (1967). An upper bound for the chroatic nuber of a graph and its 11

12 application to tietabling probles. The Coputer Journal pp CPLEX 10.1, Marina, M.K., and Das, S.R., (2001). On-Deand Multi Path Distance Vector Routing in Ad Hoc Networs. Proceedings of the Ninth International Conference on Networ Protocols, p Nasipuri, A., Casta, R., and Das, S.R., (2001). Perforance of Multipath Routing for On-Deand Protocols in Mobile Ad Hoc Networs. Mobile Networs and Applications, vol.6, no.4, pp Raachandran, K.N., Belding, E.M., Aleroth, K.C., Buddhiot, M.M., (2007). Interference-Aware Channel Assignent in Multi-Radio Wireless Mesh Networs. IEEE Infoco. 18.Prabhu, A., Gupta, H., Das, S., (2008). Miniu Interference Channel Assignent in Multiradio Wireless Mesh Networs. IEEE Transactions on Mobile Coputing. 19.Lin, K.C.-J., Chou, C.-F., (2009). Exploiting ultiple rates to axiize the throughput of wireless esh networs. IEEE Transactions on Wireless Counications. 20. Bononi, L., Felice, M.D., Molinaro, A., Pizzi, S., (2009) A cross-layer architecture for efficient ultihop counication in ulti-channel ulti-radio wireless esh networs. IEEE SECON Worshops 21. Huang, R., Ki, S., Zhang, C., Fang, Y., (2009). Exploiting the capacity of ultichannel ultiradio wireless esh networs. IEEE Transactions on Vehicular Technology. 22.Nasipuri, A., Das, S., (1999). On-deand ultipath routing for obile ad hoc networs. Coputer Counication Networs. 23.Tsai, J., Moors, T., (2006). A Review of Multipath Routing Protocols: Fro Wireless Ad Hoc to Mesh Networs. Proc. ACoRN Early Career Researcher Worshop on Wireless Multihop Networing. 12

13 Table 2 Siulation result 13