Novel Placement Mesh Router Approach for Wireless Mesh Network

Transcription

1 Novel Placement Mesh Router Approach for Wireless Mesh Network Mohsen Rezaei 1, Mehdi Agha Sarram 2,Vali Derhami 3,and Hossein Mahboob Sarvestani 4 Electrical and Computer Engineering Department, Yazd University, Yazd, Iran 1 mohsen_rezaei@ stu.yazduni.ac.ir 2 mehdi.sarram@yazduni.ac.ir 3 vderhami@yazduni.ac.ir 4 mahboob@stu.yazduni.ac.ir Abstract - Wireless Mesh Networks due their cost-efficient and fast deployment have had important networking infrastructure. Major problem in Wireless Mesh Networks, is Mesh router placement. An optimal Mesh router placement can ensure desire network performance in terms of network connectivity and coverage area. Since the problem is NP hard, to solve mesh router placement problem and achieve optimal solution with suitable quality, we can use heuristic approach. In this paper, we proposed a Genetic algorithm beside approach that has derived from circle packing problem. Circle packing problem consists in packing n non-identical circles without overlap inside the smallest containing circle C. Our model use of two objectives, maximization both network connectivity and coverage area. We have experimentally evaluated the proposed approach on instance network. The experimental results showed the efficiency of our approach for achieving high quality and optimal solutions of mesh router nodes placement in WMN. Keywords: Mesh router placement, Genetic algorithm, circle packing problem, network connectivity and coverage area. 1 Introduction A wireless mesh network (WMN) is a communications network made up of radio nodes planned in a mesh topology. In Wireless mesh networks (WMNs) there are two types of nodes: mesh routers and mesh clients. A set of mesh routers (MRs), connecting to each other wirelessly and forming a backbone to serve set of mesh clients[1]. A few MRs with the Internet connections act as Internet Gateways (IGWs) to pass on the traffic between the Internet and the WMN. Low cost design nature and fast deployment of WMNs is that make them a cost-effective option to providing wireless Internet connectivity for mobile users at anytime and anywhere. These characteristics especially would be useful in developing regions or countries, avoiding costs of deployment and maintenance of wired Internet infrastructures. The good performance and operability of WMNs largely depends on placement of mesh routers nodes in the geographical area to achieve network connectivity, stability and user coverage. The objective is to find an optimal and strong topology of the mesh network to support requirement services to clients. However, in a real deployment of WMN the automatic or purely random node placements produce poor performance WMN since the resulting placement could be far from optimal. Further, real deployment of WMNs may require taking into account specific restrictions and characteristics of real geographic area and therefore one need to explore different topologies for placing mesh routers. In fact, node placement can be seen as a crucial design and management issue in WMNs. A practical MR placement scheme should determine the positions of MRs to satisfy the following three basic requirements: (1) Maximizing network coverage: MRs should be placed as far away from each other as possible to cover more areas. However, a MR placement only considering coverage requirement could lead to insufficient network connectivity. (2) Maintaining network connectivity: Each MR can communicate with one IGW through single or multi-hop wireless links. Should there are at least one path between an each two MRs. Therefore graph of network should be connective graph. (3) Adapting to network environment: MR placement is constrained by network environment. One important environmental limitation is geographical constraint and another is traffic distribution. The nature of the environment dictates where MRs could be placed. Traffic distribution influences the number of MRs. This scheme will become more important if do two following issue: (1) Determining optimal numbers of mesh routers to maximize coverage area and connectivity. (2) Determining optimal placement of mesh routers for maximization two above objectives. Compared to the previous works, our approach makes the following improvement: Firstly, do 2 issue above, that s, determine number of mesh router needed to coverage environment of network. Do this with circle packing algorithm, that numbers of

2 mesh router used to coverage network too many lower of other researches. Secondly, due to low number of MRs used in network, cost of development and deployment in WMNs reduce proportionally. The rest of the paper is organized as follows: In Section 2, we briefly discuss the existing work in the literature. In Section 3, the network model and problem formulation is described. Circle packing problem describe in section 4. In Section 5, we give a genetic algorithm based on circle packing problem for our problem. In Section 6, we evaluate our approach and finally, we conclude the paper in Section 7. 2 Related work Unfortunately, node placement problems are shown to be computationally hard to solve to optimality [2-4], and therefore heuristic and meta-heuristic approaches are the de facto approach to solve the problem for practical purposes. Several heuristic approaches are found in the literature for node placement problems in WMNs [5-8]. In these papers, used of simulated annealing algorithm, Genetic algorithm, local search algorithm and neighborhood search methods respectively for addressing router nodes placements in wireless mesh network. In [9], author Partitioned the deployment area into grids, that used for counting the number of users and measuring the signal strength received from each mesh node. For measurement and estimate the received signal strength at each position used of the channel pathloss model. The pathloss describes the attenuation experienced by the wireless signal as a function of distance. A local searching algorithm used to find the best locations through candidate locations and its method based on probability model. In [10] the problem is addressed under a constraint network model in which the traffic demand is nonuniformly distributed and the candidate positions for MRs are pre-decided. Authors proposed a heuristic algorithm to obtain a close-to-optimal solution to reduce complexity of determining the locations of MRs while satisfying the traffic constraint. A 2-stages multi objective evolutionary optimization algorithm which tries to optimize the two objectives by means of genetic algorithms, where individuals or solutions are represented by network graphs proposed in[11].in the first stage of MOGAMESH, candidate network topologies are found by letting a population of graphs evolve. In the second stage, a link elimination algorithm further reduces the number of links of the network. A virtual force based MR placement algorithm (VFPlace) presented in [12] which Given a certain number of mesh routers, VFPlace targets to determine the positions of these mesh routers to maximize their overall coverage and maintain a certain number of neighbors for each mesh router, while satisfying geographic and traffic constraints of a specific WMN. VFPlace tried to dynamically avoid placing mesh routers in prohibitive regions, favor preferential regions and balance the distance between mesh routers. 3 Network Model and Problem Formulation 3.1 Network Model The MR placement problem can be described as a way to determine appropriate positions for a number of MRs in a network area while satisfying environmental and traffic constraints. The area to be covered by a WMN backbone is modeled as a two-dimensional disk with a radius R in a two dimension coordinate plane. The center of disk is located at (0, 0), the origin of the coordinate system. At first, define a node set of MRs name. {v,v,,v n- that each node represent a mesh router. We show each mesh router with a circle. We consider transmission range of each mesh router as radius of related circle. Then we denote geographical constraints area set with {v n,v n,,v n c that each node represents a circle area, which MRs can t be placed inside in. Given any nodev, its position is represented with the coordinate x i. For a MR node x i is the position where the MR is situated. In other words, represent a center of v i circle. Since we consider one IGW in this paper, is located in, Two mesh router nodes are connected if the Euclidean distance between them is no longer than the MR s transmission range. In other words, two mesh router (circle) connected if have overlap with each other. The coverage area of a node v i, prime of circle v. It should be also noted that routers are assumed to have different radio coverage and higher radio coverage router assume to have more capacity and powerful addresses. 3.2 Problem Formulation Determination placement of MR nodes has to minimize the required number of MR nodes needed to meet the maximize coverage as possible, full connectivity, and environmental constraints for network. The minimum number of MRs has great effect to maximally reduce the investment cost imposed by MR hardware. Based on the

3 above network, we formulate the MR placement problem is to find the optimal placement by following inequalities: v i (v i ) R 2 i, v i (1) R ij v i, v j (2) (x i,y i ) (x c,y c ), i, c (3) Inequality (1) says the set of selected MR nodes provide maximize coverage as possible of the network domain and inequality (2) models the full connectivity of all nodes. Full connectivity implies that every node to be connected to the IGW by at least one path and exist one path at least between any two nodes in network where R ij denote distance a path between node v i, v j. Inequality (3) to satisfy geographical constraints says the position of mesh nodes shouldn t inside set. 4 Circle Packing Problem Cutting and Packing (C&P) problems are scientifically challenging problems with a wide spectrum of applications [13 17]. They are very interesting NP-hard combinatorial optimization problems; i.e., no procedure is able to exactly solve C&P problems in polynomial time. They generally consist of packing a set of items of known dimensions into one or more large objects or containers as to minimize the unused part of the objects or waste. The items and objects can be rectangular, circular, or irregular. In this paper, we use of the problem of packing a set of circular items into the smallest circle. The circular packing problem (CPP) consists of packing a set {,2,,n- } of non-identical circles i without overlap into the smallest containing circle C where each iis characterized by its radius r i The goal is to search for the best packing of the n circles into C, where the best packing minimizes waste. Instance of circle packing problem showed in Fig. 1. Fig. 1- Instance of Circle Packing Problem CPP is equivalent to finding the coordinates x i of every circle i, i and the radius r and coordinates x,y of C, such that no pair ( i, j ), and i j overlap. Formally, the problem can be stated as finding the optimal level of the decision variables r, x, y, and x i, i, that Minimize r (CPP) ubject to (x i -x) 2 (y i -y) 2 r-r, i, (4) (x i -x) 2 (y i -y) 2 r i r j, i, j<i CPP has a linear objective function but non-linear nondifferentiable constraints. The first set of constraints states that any i, i is totally contained within C. There are n of these constraints, one for each i. The second set reinforces the no overlap constraint of any pair of distinct circles ( i, j ); that is, the Euclidean distance between the centers of i and j must be greater than or equal to (r i r j ). In circle packing problem as mentioned above, one of conditions, is c rcles shouldn t have overlap with each other. in order that we can use this algorithm for our problem, need to change this condition such that each circle (router) overlap with at least one other circle (router) to satisfy network connectivity condition. Thus we modify algorithm in determine position such that any circle overlap with two other circles. The resulted pattern has the following key properties: The final network is formed by n circles. Each MR is placed in the center of each circle. Each circle is surrounded by at most six other circles to cover the disk without gaps. The distance between any two neighboring MR nodes i and j is smaller than the sum of transmission range s, r i r j, so that the network connectivity is guaranteed. Our approach based on circle packing pattern fills the network plane with limited overlaps and no gaps. Overlaps are necessary to satisfy the connectivity requirement, limited overlaps essential for minimizing the number of MRs in the disk; no gap is needed to satisfy the coverage requirement. 5 Our Genetic Algorithm Based on Circle Packing Problem In our approach, we present modified version of circle packing algorithm and solve it with genetic algorithm so that use for placement mesh routers problem in WMNs.

4 5.1 Encoding We use a permutation of (,2,,n) to code a individual for encoding. M individuals are randomly generated to form the initial population. We run GA with different value of n. for obtain optimal number of routers, we call genetic algorithm with different value for n, and calculate coverage area for any pattern obtained with these value of n. each chromosome denotes a router. 5.2 Fitness function The fitness function is of particular importance in GAs as it guides the search towards most promising areas of the solution space. Furthermore, in our case, although we face an optimization problem with multiple criteria, including connectivity of MRs and coverage area and therefore the fitness function in our particular case can be expressed in different ways. Since positioning algorithm, placed routers in positions that have overlap at least with one other router, thus we can use ratio of total coverage area each individual to evaluate fitness of it. This means that proportion total coverage area to number of routers used to achieve this coverage. If two patterns have same total coverage area, we calculate the numbers of router in pattern and pattern with lower router has greater fitness. 5.3 Crossover operators We apply a crossover operation that retains the validity of permutations [18]. For convenience, we assume K is an even number, so we have K/2 pairs of parents. For each pair of parents, we apply the crossover operation to generate two children. In this paper, we apply crossover as follows: child 1 and child 2 area pair of parent solutions. Suppose q is a random integer, where 1 q n. The first child is generated by taking routers q from child 1 and appending to this subsequence any missing routers in the order in which they appear inchild 2. The second child is obtained in the same way, only with first subsequence taken from child 2, and the remainder being made up from child 1. located at (0, 0), the center of the network disk and doesn t shows in Figures. As mentioned above and described in next section, we consider value R 2 /r 2 for initial and during algorithm increase its value. Fig. 2 shows the result of placement our algorithm in the case of geographical constraints doesn t consider. At compare with Fig. 4 that show random placement and use of 38 nodes, our result can get to coverage area close to 95% with only 24 nodes (router) rather than 38 nodes. Fig. 2-MR placement without geographical constraints Geographical constraints, places that cause to condition node can t be placed in these regions as shown in Fig. 3, considered and coverage area 90% obtained again with 24 nodes. Rather than Fig. 5 that with 38 nodes coverage network, our approach with 24 nodes, this mean with 14 nosed less, almost entire network coverage. This reduce in number of router needed to coverage network, Significantly decrease cost of network, consist of installing, deployment, maintenance. In others word, cost of hardware of mesh network 36% has reduced than [12] Mutation operators We randomly select two routers from its sequence and exchange their positions as mutation operator. 6 Simulation Result In this section, we present the simulation results to show the effectiveness of our approach. The simulation is done using the Matlab. For compare our result with [12], used of same scenario network in simulation, that s: The radius of the network domain is 8 units (R = 8). The transmission range of each MR node is 2 units (r = 2). But transmission MRs can be different. The number of MR nodes to be placed determine by our approach. The IGW Fig. 3- MR placement with considering geographical constraints

5 In terms of network connectivity, since our algorithm use of method that each node at least has overlap with another node, full connectivity 100% obtain and between all of the nodes exist path. While in Fig. 4 random placement presented in [12], full connectivity doesn t exist. Fig. 4-Random Placement algorithm as mention in genetic algorithm section, have two phases. In first phase consider all if routers with identical and based on placement done. After placement, we calculate traffic loads that each router must passed and if traffic loads one router beyond its capacity, algorithm alters this router with powerful router that have more capacity and higher transmission range. In phase continue to replace weaker router with powerful router and thus the position of these routers to be constant. Since position of these routers determined, algorithm restarts for other nodes and adds MRs one by one to network domain till get total coverage close to 100% and re-determine their final position of these nodes. Thus number of MRs according to this approach can be obtained that consist of some routers with distinct transmission range. In Fig. 6 shows the case of, router s number 2 in Fig. 3), after calculation traffic load, exchange with powerful router, that s o. 8 router. Fig. 5-MR placement by [12] 6.1 Finding Optimal Number of Mesh Routers If we consider transmission range of mesh router (radius circle) identical, and assume any two mesh router don t have overlap with each other, at least R 2 /r 2 MRs required to coverage network area (if position of circles determine with circle packing problem but it is clear don t get full coverage in this case because the circles don t have overlap with each other and thus exist gap in network disk. We in our approach to find the optimal number of MRs to coverage network consider two cases: 1) all of mesh routers have same transmission range and 2) routers have different transmission range. In case 1, algorithm with R 2 /r 2 MRs that have overlaps started and one by one add MR to network till total coverage of pattern close to 100%, because the area related to geographical constraint set prevent to get to full coverage in some case based on position of member set VC. If we use of routers with different coverage radio, problem different partly. In our Fig. 6-Find number of routers after traffic load phase 7 Conclusion In this work we have presented Genetic Algorithm based on circle packing problem for the problem of mesh router nodes placement in Wireless Mesh Networks (WMNs). We have considered two metric for evaluation our solution: network connectivity, and ration of network coverage area. Experimental results showed in network connectivity, obtained 100% connectivity, and in coverage area with many lower number mesh routers, coverage area close to 100% obtained. In fact, with reduce number of needed mesh router; cost of setup, investments decrease significantly. The proposed approach has practical usefulness for designing and deploying of real WMNs. In our future work we would like to improve our approach to get 100% coverage.

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