ACO and PSO Algorithms Applied to Gateway Placement Optimization in Wireless Mesh Networks

Transcription

1 2012 International Conference on Networks and Information (ICNI 2012) IPCSIT vol. 57 (2012) (2012) IACSIT Press, Sinapore DOI: /IPCSIT.2012.V57.02 ACO and PSO Alorithms Applied to Gateway Placement Optimization in Wireless Mesh Networks Dac-Nhuon Le 1, Nhu Gia Nuyen 2, Nuyen Dan Le 1, Nhia Huu Dinh 3 and Vinh Tron Le 4 1 Faculty of Information Technoloy, Haiphon University, Vietnam 2 Duytan University, Danan, Vietnam 3 School of Graduate Studies, Vietnam National University, Vietnam 4 Hanoi University of Science, Vietnam National University Abstract. In this paper, we study the challenin problem of optimizin ateway placement for throuhput in Wireless Mesh Networks and propose a novel alorithm based on Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) for it. A ateway placement alorithm was proposed based on ACO, we enerate the locations of ateway randomly and independently then calculate the probability and pheromone values of ants will choose to o from current ateway i to next client. After each iteration, the pheromone values are updated by all the number of ants that have reached to the destination successfully and found the optimal solution. Our alorithm was proposed based on PSO, we calculate the fitness value of each scheme and update them step by step with the best method to quickly find the optimal. Numerical results show that the proposed alorithm has achieved much better than previous studies. Keywords: Wireless Mesh Networks, Gateway Placement, Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO). 1. Introduction A wireless mesh network (WMN) is a communication network made up of radio nodes oranized in a mesh topoloy, which often consists of mesh clients, mesh routers and ateways [1]. The mesh clients are often laptops, cell phones and other wireless devices, which are connected to the Internet throuh the mesh routers. The mesh routers forward traffic to and from the ateways which connected to the Internet. The coverae area of the radio nodes workin as a sinle network is sometimes called a mesh cloud. Access to this mesh cloud is dependent on the radio nodes workin in harmony with each other to create a radio network. A mesh network is reliable and offers redundancy. When one node can no loner operate, the rest of the nodes can still communicate with each other, directly or throuh one or more intermediate nodes. Wireless mesh networks can be implemented with various wireless technoloy includin , , cellular technoloies or combinations of more than one type. Fi.1. A typical WMN 8

2 A wireless mesh network has some features which are similar to wireless ad-hoc network. It is often assumed that all nodes in a wireless mesh network are immobile but this is not necessary. The mesh routers may be hihly mobile and are not limited to power, memory, calculatin ability and operate as intellient switchin devices. Fi. 1 presents an example of a WMN. In recent years, the optimizin WMN problem is interested in many researches. However it still remains open [1]. In there, ateway placement is the most interested problem in optimizin WMN. There are some analoous research results in wired or cellular networks. However, all the above investiation has been focused on network connectivity of WMNs by deployin the minimum number of backbone nodes [2]. Throuhput is one of the most important parameters that affect the quality of service of WMN. So in this paper, we will improve a ateway placement alorithm to optimize throuhput for WMNs. A similar problem was studied by Pin Zhou, Xudon Wan, B. S. Mano and Ramesh Rao in [2], however, their scheme was not updated step by step, and the locations of ateways were determined sequentially, so the location of previously-placed ateways affects the location of those placed later. Constructin computation model to calculate the throuhput of WMNs is very necessary, but it is not simple to build. There are many computation models built in [3-8], but all of them, except [8], are not suitable for calculatin throuhput of WMNs. In this paper, we use the computation model in [2], in which TDMA schedulin is assumed to coordinate packet transmissions in mesh clients, mesh routers, and ateways. The rest of this paper is oranized as follows. Section 2 presents the computation model and briefly introduces the main idea of MTW-based ateway placement proposed in [2]. Section 3 presents our new alorithm for ateway placement in optimizin WMN based on ACO and PSO. Section 4 presents our simulation and analysis results, and finally, section 5 concludes this paper. 2. MTW-based Gateway Placement In this section, we first present the computation model and briefly introduce the main idea of MTWbased ateway placement proposed in [2] 2.1. Computation Model Network Topoloy The computation model presented in [2] brins out a typical WMN topoloy for Internet accessin as follows and is illustrated in Fi. 2. Router with ateway function Router without ateway function. Client Fi.2. Network topoloy of an WMN infrastructure with ateways This topoloy has N c mesh clients which are assumed to be distributed on a square R, N r routers, and N ateways with the constraint of 1 N N r N c. Accordin to [9] R is partitioned evenly into N r cells R, and a mesh router is placed in the centre of each cell. In each cell, mesh clients are connected to the mesh router like a star topoloy and are not communicated with each other directly. Data transmission is carried out amon mesh clients, which are equivalent such that they always have the same amount of packets to send or receive durin a certain time, while the mesh routers find the best route and forward data to its destination. All traffic is assumed to o throuh ateways. Each mesh router determines its nearest ateway to relay packets to or from that. If there is more than one nearest ateways, the router will load its traffic to all its nearest ateways by a round robin. A mesh client is said to be associated with a ateway if its connected 9

3 router is associated with the ateway. Thus, traffic load of a mesh client will also be shared by all its potentially associated ateways. There are some definitions of communications which will be frequently used: Local communications: it is referred as the communications between a mesh router and a mesh client; Backbone communications: it is referred as the communications between two mesh routers, which includes the communications between a ateway and a mesh router; Downlink communications: it is referred as the communications from a ateway to a mesh client, in which a data packet is first relayed amon mesh routers in backbone communications and is then sent by a mesh router to one of its connected mesh clients; Uplink communications: it is referred as the communications from a mesh client to a ateway, in which a data packet is sent in the exact reverse direction as described in the downlink communications Transmission Model Each mesh router is often equipped with two virtual radio interfaces over one physical radio interface, in which one transmittin at W 1 bits/s for backbone communications and the other transmittin at W 2 bits/s for local communications. Each mesh client transmits W 2 bits/s in local communications. It is assumed that W 1 and W 2 are orthoonal so that local communications and backbone communications do not influence each other. Moreover, mesh routers or mesh clients can receive packets from only one sender at a time. Transmission and reception can occur in either time-division duplex (TDD) or frequency division duplex (FDD), dependin on how the physical and MAC layers are implemented Throuhput The computation model proposed in [2] introduces two criterions to evaluate the performance of ateway placement alorithms: the total of throuhput and the minimal throuhput of each client. In this paper, we also use these criterions to evaluate the performance of our alorithm. Problem 1: Optimal ateway placement for maximizin areate throuhput of WMNs, i.e., in the above WMN model, iven N c, N r, N, W 1, W 2 and specific clients distribution, routers distribution, transmission, schedulin and routin protocols, N ateways are chosen amon N r mesh routers such that, N c TH(, i N ) (1) is maximized, where TH(i,N ) denotes the per client throuhput of the i th mesh client when i= 1 N ateways are deployed. Problem 2: Optimal ateway placement for maximizin the worst case of per client throuhput in the WMN, i.e., in the above WMN model, iven N c, N r, N, W 1, W 2 and specific clients distribution, routers distribution, transmission, schedulin and routin protocols, N ateways are chosen amon N r mesh routers such that, N c min TH( i, N ) (2) is maximized. i= Sharin Efficiency of Gateways IntD is defined as Interferin Distance of Gateways. If distance of two ateways less than IntD, they interfere with each other. Interferin ateways have to share the same wireless channel in the backbone communications. The alorithm to calculate the sharin efficiency of ateways is presented as follows. 1) Constructin the table of non-overlappin interferin roups arraned in descendin order of the number of elements in the roup. 2) Assinin percentae value for each ateway from the top to the last row in the above table. In the first step, any two elements of each roup that interfere with each other, and a roup appearin later must have at least one ateway which does not belon to the previous roups. The procedure that calculates percentae value for the ateways is described as follows: Assin value of 100% for all the ateways. For the top row to the last row of the table in the first step k=1/the number of ateways in current roup. 10

4 For the first ateway to the last ateway in current roup If percentae value > k then push into subroup1 Else push into subroup2. End for. 1-sum of all the percentae value in subroup2 P= the number of the ateways in subroup1 Assin value of P for all ateways in subroup1. End for. The final computin value is stored in G eff (k), k=1..n Throuhput Computation Throuhput of the i th mesh client when N ateways are deployed, denoted as TH(i,N ), is calculated as follow: { } ( ) 1( ) 2() W W TH i, N = min TH i, N, TH i, (3) i= 1... Nc Here, TH W1 (i, N ) is defined as the throuhput of the i th mesh client in backbone communications and TH W2 (i) is defined as the throuhput of i th mesh client in local communications. Because W 1 and W 2 are orthoonal, so we can compute TH W1 (i, N ) and TH W2 (i) separately. Note that TH W2 (i) is independent of N in WMN model and if a mesh client is connected directly to a ateway, its throuhput is decided only by the per-client throuhput in local communications. TH W1 (i, N ) is computed as follows: TH W1 (, i N ) = k = all theassociated ateways withthemeshrouter R N ( ) TH '( k) Here, N () is the number of ateways associated with the mesh router R. A ateway is associated with a router if the distance between them is less than or equal the radius of that ateway. The computation of the radius of ateway is proposed in sub-section TH (k) is the throuhput per client that the k th ateway can uarantee for all its associated mesh clients in backbone communications. Geff ( k) cw 1 1 (5) TH '( k) = ( N ( l) N '( l) N ( l)) c l = all associated routers th with the k ateway hop Here c 1 W 1 is the throuhput that the k th ateway can uarantee in backbone communications, N c (l) is the number of clients associated with the mesh l th router. N hop (l) is the actual time slot that the R l -connected mesh client uses to transmit data to the ateway. N hop ()=N hop (), if N hop () < SRD; N hop ()=SRD, if N hop () SRD; (6) Here, N hop () is the number of hops from the mesh client to the ateway. SRD is defined as Slot Reuse cw 2 2 Distance. Next, TH W2 (i) is computed simply as follows: THW () i =, i = 1.. N 2 c (7). Here, c 2 W 2 CRF Nc ( ) is the throuhput that R can uarantee for all associated mesh clients. CRF is defined as Cell Reuse Factor The oriinal MTW-based Gateway Placement In this alorithm, a traffic-flow weiht, denoted as MTW(), is calculated iteratively on the mesh router R, =1..N r. Each time, the router with the hihest weiht will be chosen to place a ateway. The weiht computation is adaptive to the followin factors: 1. The number of mesh routers and the number of ateways. 2. Traffic demands from mesh clients. 3. The location of existin ateways in the network. 4. The interference from existin ateways. (4) 11

5 Nr First of all, this alorithm proposes a formula to compute the ateway radius: R = round( ) (8) 2 N Assumin all mesh clients are similar in WMN model, then local traffic demand on each mesh router, denoted as D(), =1..N r, represented by the number of mesh clients connected to R. MTW() is calculated with D() and R as follows: MTW()=( R+1) D() + R (traffic demand on all 1-hop neihbors of R ) + (R-1) (traffic demand on all 2-hop neihbors of R ) +(R-2) (traffic demand on all 3-hop neihbors of R ) + Place the first ateway on the router with hihest MTW(). If more than one ateways are requested, readust D(), =1..N r with R as follows: set the value 0 for all routers within (R -1) hops away from R (includin R ) and reduce to half for ateways which are R hops away from R. Re-calculate MTW() with the new D(), and perform the followin procedure. 1. Choose the router with the hihest weiht as potential location for ateway placement, namely R. 2. Re-construct the table of non-overlappin interfere roups with R and previous ateways. 3. Compute the sharin efficiency for R. 4. MTW () = MTW() G eff ()MTW (). If MTW () is still larer than the second hihest weiht, then place the ateway in the location. Otherwise, repeat the above steps from 1 to 5 until obtainin the location 3. Optimizin Gateway Placement in WMN usin ACO and PSO 3.1. Apply ACO alorithm to Gateway Placement Problem The ACO alorithm is oriinated from ant behavior in the food searchin. When an ant travels throuh paths, from nest food location, it drops pheromone. Accordin to the pheromone concentration the other ants choose appropriate path. The paths with the reatest pheromone concentration are the shortest ways to the food. The optimization alorithm can be developed from such ant behavior. The first ACO alorithm was the Ant System [10], and after then, other implementations of the alorithm have been developed [11-12]. In our case the pheromone matrix is enerated with matrix elements that represent a location for ant movement, and in the same time it is possible receiver location. Assume that the WMN model, presented in Section II-1, is divided into N cells and numbered from left to riht and from top to bottom. In this paper, we use inteer encodin to express an element of matrix A m*n (where m is the number of ateways, n is number of client). a i will then receive a random inteer enerated correlatively. The pseudo code of the procedure for each element (1) Determine the location of ateways. (2) Compute the throuhput achieved. The ant population is randomly enerated (50 ants) and each ant is associated to one matrix location (node). Location of ants is an inteer, randomly enerated, correspondin to the interval of [0, N-1]. The next node (location) is selected accordin to the probability with which ant k will choose to o from current ateway i to next client is calculated by the followin formula: p k i = α β τ i η i α β τi ηi k l Ni (9) k In which, τ i is the pheromone content of the path from ateway i to client, N i is the neihbourhood includes only locations that have not been visited by ant k when it is at ateway i, η i is the desirability of client, and it depends of optimization oal so it can be our cost function. The influence of the pheromone concentration to the probability value is presented by the constant α, while constant β do the same for the desirability. These constants are determined empirically and our values are α=1, β=10. The ants deposit pheromone on the locations they visited accordin to the relation. τ = τ +Δ τ (10) new current k 12

6 where k Δ τ is the amount of pheromone that ant k exudes to the client when it is oin from ateway i to client. This additional amount of pheromone is defined by k 1 Δ τ = (11) f Where f is the cost function of the client is computed by the formula (3). The pheromone evaporates durin time and diminishes if there are no new additions. The pheromone evaporation is applied to all locations as follows: new ( 1 ) ( 0 1) τ = ρ τ < ρ (12) The value of ρ is selected empirically, what is in our case ρ= Apply PSO alorithm to Gateway Placement Problem Particle Swarm Optimization (PSO) was invented by Kennedy and Eberhart [15-16] while attemptin to simulate the choreoraphed, raceful motion of swarms of birds as part of a socio conitive study investiatin the notion of collective intellience in bioloical populations. There are three common types of expressin an element: encodin as a real number, an inteer and a binary. In this paper, we use inteer encodin to express an element. An element is a K-dimensional vector (K is the number of ateways), where each of its component is an inteer correspondin to the position to be located in the WMN. Specifically, ateways are denoted by { 1,, k }, in which if the th element is {a 1,, a k} then a i would correspond to the ateway i, and its value will be a random inteer enerated correlatively. Assume that the WMN model, presented in Section 2.1, is divided into N cells and numbered from left to riht and from top to bottom. a i will then receive the value in the rane of [0..(N-1)]. The initial population is enerated with P elements (P is a desinated parameter). Each element is a K- dimensional vector (K is the number of ateways) that each component is an inteer, randomly enerated, correspondin to the interval of [0,N-1]. Fitness value of th element is calculated by the followin formula: F = 1 N c i= 1 1 TH (, i K) In which, N c is the number of clients, K is the number of ateways, TH(i,K) is computed by the formula (3). Elements in each eneration are updated accordin to formula (14) and (15) described below. In which present[] and v[] are respectively the th element in the current eneration and its speed. In the context of the current problem, present[] and v[] are K-dimensional vectors. v[] = v[] + c1 * rand() * (pbest[] - present[]) + c2 * rand() * (best[] - present[]) (14) present[] = present [] + v[] (15) Since PSO is a stochastic process, we must define the conditions for stoppin the alorithm. The alorithm will stop after G enerations (G is a desin parameter) or when the values of Best and pbest are unmodified. Our results have been published in [13-14]. 4. Numerical Results and Discussion Accordin to numeric results in [2], the MTW-based Gateway Placement Alorithm is better than three ateway placement alorithms: Random Placement (RDP), Busiest Router Placement (BRP), and Reular Placement (RGP). Therefore in this paper we only compare our alorithm with MTW-based ateway placement alorithm. We study two experiments. In the first experiment we assume N c =200, N r =36, l=1000m, i.e. there are 200 mesh clients distributed in a square reion of 1000m x 1000m; the square is split evenly into 36 small square cells and a mesh router is placed in the centre of each cell. Concurrently, we assume CRF = 4, SRD=3, IntD=2, the backbone bandwidth is 20Mbps and the local bandwidth is 10Mbps. The second experiment is (13) 13

7 similar to the first one, but in which N c =400, N r =64. The local traffic demand of each mesh router in all experiments is enerated randomly. In each experiment, we optimize the ateway placement problem by maximum one of two parameters: the total throuhput of all mesh clients, denoted as ACO_Sum, PSO_Sum, and the minimal throuhput of each mesh client, denoted as ACO_Min, PSO Min. Then we compare our results with the results achieved by MTW-based ateway placement alorithm. Firstly, we compare the areate throuhput and the worst case throuhput achieved by each alorithm, as shown in Fi. 3 and Fi. 4. (a) (b) (a) (b) Our alorithm based on ACO Our alorithm based on PSO Fi. 3. The comparison of the areate throuhput (a) and the worst case of per client throuhput (b) in the first experiment (a) (b) (a) (b) Our alorithm based on ACO Our alorithm based on PSO Fi. 4. The comparison of the areate throuhput (a) and the worst case of per client throuhput (b) in the second experiment We find that the results achieved by our alorithm are better than the results achieved by MTWP alorithm in all experiments. Next, we easily realize the fact that when the number of ateways increase, the throuhput miht not be better. So when desinin the WMN, it is necessary to choice the number of ateways suitably to maximum the throuhput of WMN and reduces the cost. Final, we compare throuhput per ateway of two ateway placement alorithm, as shown in Fi. 5. (a) The first experiment (b) the second experiment (a) The first experiment (b) the second experiment Our alorithm based on ACO Our alorithm based on PSO Fi. 5. The comparison of the areate throuhput per ateway The results show us once aain the superiority of the alorithm proposed in this paper. The results show that PSO has better properties compared to ACO alorithm. 5. Conclusion The problem of ateway placement in WMNs for enhancin throuhput was investiated continuously in this paper. A ateway placement alorithm was proposed based on ACO, PSO. A non-asymptotic analytical 14

8 model was also derived to determine the achieved throuhput by a ateway placement alorithm. Based on such a model, the performance of the proposed ateway placement alorithm was evaluated. Numerical results show that the proposed alorithm has achieved much better performance than other schemes. It is also proved to be a cost-effective solution. The best performance we ot with the PSO alorithm with the lowest cost function and consumin time. While the ACO alorithm doesn t converes as fast and its results is litter worse than PSO. Optimizin ateway placement toether with throuhput maximization is our next research oal. 6. References [1] F. Akyildiz, Xudon Wan, Weilin Wan: "Wireless mesh networks: a survey", "Computer Networks and ISDN Systems", vol.47 no.4, pp , 15 March [2] Pin Zhou, Xudon Wan, B. S. Mano and Ramesh Rao (2010), On Optimizin Gateway Placement for Throuhput in Wireless Mesh Networks, Journal on Wireless Communications and Networkin Volume 2010 (2010), Article ID , 12 paes doi: /2010/ [3] P. Gupta and P. R. Kumar, Internets in the sky: The capacity of three dimensional wireless networks, Commun. Inform and Syst., vol.1, no. 1, pp , Jan [4] M. Grosslauser and D. Tse, Mobility increases the capacity of ad-hoc wireless networks, in Proc IEEE INFOCOM 01, [5] B. Liu, Z. Liu and D. Towsley, On the capacity of hybrid wireless networks, in Proc IEEE INFOCOM 03, [6] U. C. Kozat and L. Tassiulas, Throuhput capacity of random ad hoc networks with infrastructure support, in Proc ACM MOBICOM 03, [7] A. Zemlianov and G. de Veciana, Capacity of ad hoc wireless networks with infrastructure support, IEEE J. Sel. Areas Commun., vol.23, no.3, pp , Mar [8] P. Zhou, X.Wan, and.r. Rao, Asymptotic Capacity of Infrastructure Wireless Mesh Networks, IEEE Transaction on Mobile Computin, vol. 7, no.8, pp , Au [9] J. Robinson and E. Knihtly, A Performance Study on Deployment Factors in Wireless Mesh Networks, in Proc. IEEE Infocom 2007, pp , May [10] M. Dorio, V. Maniezzo, and A. Colorni, "Ant system: Optimization by a colony of cooperatin aents", IEEE Trans. on System, MAN, and Cybernetics-Part B, vol. 26, pp , February 1996 [11] E. Rao-Ilesias, O. Quevedo-Teruel, "Linear Array Synthesis usin an Ant Colony Optimization based Alorithm", IEEE Trans. on Antennas and Propaation, [12] M. Dorio, M. Birattari, and T. Stitzle, Ant Colony Optimization: Artificial Ants as a Computational Intellience Technique, IEEE computational intellience maazine, November, [13] Vinh Tron Le, Nhia Huu Dinh, Nhu Gia Nuyen, The minimum numbers of ateway for maximizin throuhput in wireless mesh networks, in Proc. 2 nd International Symposium on Information and Communication Technoloy (SoICT 2011), Ha Noi, Viet Nam, [14] Vinh Tron Le, Nhu Gia Nuyen, Dinh Huu Nhia, A Novel PSO-Based Alorithm for Gateway Placement in Wireless Mesh Networks, in Proc, 3 rd IEEE International Conference on Communication Software and Networks (ICCSN), China, 2011, pp [15] James Kennedy and Russell Eberhart, Particle swarm optimization in Proceedins of IEEE International Conference on Neural Networks, paes , Piscataway, NJ, USA, [16] 15