# Efficient Load Balancing Routing in Wireless Mesh Networks

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3 Figure.1. Example mesh network The delay is also of great importance in the practical WMN, we incorporate the delay term into objective function. To do this, we define the delay penalty function for each flow, which penalizes the objective function foe selecting the route with long end to end delay. IV. PROPOSED LOAD-AWARE ROUTING SCHEME In this section, we design the routing seheme by using the dual decomposition method. We first formulate the optimization problem from the objective function and constraints introduced in the previous section, and derive the dual problem. Next, we explain how to calculate the flow data rate vector for the given Lagrange multipliers, and suggest the subgradient method to iteratively calculate the optimal Lagrange multipliers. Finally we propose the dampening algorithm to alleviate the route flapping problem. A. Problem formulation We formulate the optimization problem from air time ratio, β and mergerd objective function. We solve the optimization problem by converting it to the dual problem according to the Lagrangian method. From the Lagrangian, we define the dual function. From the dual function, we define the dual problem. We can find optimal solution from this problem. B. Flow data rate calculation for given lagrange multipliers We calculate the flow data rates that maximizes the Lagrangian for given Lagrange multipliers. Proposition 1: The set of flow data rate vector contains at least one single path flow data rate vector. Proof: consider the any flow data rate. Let flow data rate be the flow data rate vector such that for the active route that minimizes link cost. This means there exists a single path floe data rate vector. C. Lagrange multiplier update We will find the solution of the dual problem. The constraint in the dual problem can be incorporated into the dual function. We define the modified dual function where satisfies the constraint for given Lagrange multiplier. D. Convergence of flow data rate We will take the flow data rate vector as the estimation of the optimal flow data rate vector at jth iteration. We will discuss the convergence of this flow data rate vector. Since the optimization problem is strictly feasible and the objective and constraint functions are concave, the strong duality holds from slater s constraint qualification. V. DISTRIBUTED IMPLEMENTATION For implementation, one node with in a cluster is designated as the head of the cluster. The head of the cluster is assumed to be able to communicate with the transmitter nodes of the links in its cluster. The proposed scheme takes the following steps at the jth iteration of the sungradient method. Fig. 2 illustrates an example of control information exchange for this operation. Open Access Journal Page 40

5 B No gateway scenario Fig.6. System throughput according to the number of flows in the no gateway scenario. VII. CONCLUSIONS In this paper, we have developed a load aware routing scheme for the WMN. We have formulated the routing problem as an optimization problem, and have solved it by using the dual decomposition method. The dual decomposition method makes it possible to design a distributed routing scheme. However, there could be a route flapping problem in the distributed scheme. To tackle this problem, we have suggested a dampening algorithm and have analyzed the performance of the algorithm. The numerical results show the proposed scheme with a dampening algorithm well converges to a stable state, and achieves much higher throughput than the ETT-based scheme does owing to its load-balancing capacity. FUTURE ENHANCEMENT The proposed scheme can be applied to various single band PHY/MAC layer protocols. In future work, we can extend the proposed scheme so that we can applied to the multiband protocols, which can provide larger band width to the WMN. REFERENCES [1] R. Bruno, M. Conti, and E. Gregori, Mesh Networks: Commodity Multihop Ad Hoc Networks, IEEE Comm. Magazine, vol. 43, no. 3,pp , Mar [2] D. De Couto, D. Aguayo, J. Bicket, and R. Morris, High-Throughput Path Metric for Multi-Hop Wireless Routing, Proc. ACM MobiCom, Sept [3] D. Passos, D.V. Teixeira, D.C. Muchaluat-Saade, L.C.S. Magalhaes,and C.V.N. Albuquerque, Mesh Network Performance Measurements, Proc. Int l Information and Telecomm. Technologies Symp.,Dec [4] B. Awerbuch, D. Holmer, and H. Rubens, The Medium Time Metric: High Throughput Route Selection in Multi-Rate Ad Hoc Wireless Networks, Mobile Networks and Applications, vol. 11, no. 2, pp , Apr [5] R. Draves, J. Padhye, and B. Zill, Routing in Multi-Radio, Multi-Hop Wireless Mesh Networks, Proc. ACM MobiCom, Sept [6] Y. Yang, J. Wang, and R. Kravets, Designing Routing Metrics for Mesh Networks, Proc. IEEE Workshop Wireless Mesh Networks, Sept [7] A.P. Subramanian, M.M. Buddhikot, and S.C. Miller, Interference Aware Routing in Multi-Radio Wireless Mesh Networks, Proc. IEEE Workshop Wireless Mesh Networks, Sept [8] C.E. Koksal and H. Balakrishnan, Quality-Aware Routing Metrics for Time-Varying Wireless Mesh Networks, IEEE J. Selected Areas in Comm., vol. 24, no. 11, pp , Nov [9] S.J. Lee and M. Gerla, Dynamic Load-Aware Routing in Ad Hoc Networks, Proc. IEEE Int l Conf. Comm., June Open Access Journal Page 42

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