**1. Introduction**

Wireless mesh networks (WMNs) are attractively deployed as a backhaul for public Internet access with the advantages of network performance and cost efficiency. With the cooperation of multiple mesh nodes, a packet is transmitted through multi-hops to reach a destination. Wireless medium experiences relatively an unstable environment due to interferences of wireless signals. As traffic increases, a communication environment becomes worse. Similarly, as more mesh nodes join a WMN, a network performance is also degraded due to increasing interferences. Therefore, challenges of a WMN are how to accommodate a dynamic nature of wireless medium and achieve the scalability.

A typical WMN serves hub-and-spoke type accesses, where a mesh gateway (hub) connects to the Internet for mesh clients as shown in Fig. 1. In other words, a mesh node is required to communicate with just one-of-many mesh gateways similar to anycast communications [1, 2]. For anycasting, conventional routing schemes [3–5] are developed with modifications of existing unicast routing protocols. That is, the schemes usually select the closest destination among multiple service gateways. Thus, they are inefficient in taking benefits of having multiple gateways. Even though some protocols [6–8] utilize multiple gateways for load balancing, they convey flooding overheads to collect traffic load information for re-routing and require associations among the gateways.

Classically, back-pressure routing [9] and geographic routing [10] are considered as alternatives for traditional hop-count-based routing. Back-pressure routing is well-known to achieve throughput-optimal by adaptively selecting paths depending on queuing-dynamics. However, it unnecessarily chooses long paths and degrades network performance by keeping old data packets. This problem manifests critically in lightly- or moderately-loaded cases [11]. On the other hand, conventional geographic routing is scalable with no flooding overhead, but it is vulnerable to avoiding congested hot spots due to its simple geographical routing metric. Even though some enhancements of geographic routing for congestion mitigation, it entails similar overheads such as perimeter routing or other face routing.

©2012 Jung, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 Will-be-set-by-IN-TECH 134 Wireless Mesh Networks – Effi cient Link Scheduling, Channel Assignment and Network Planning Strategies Autonomous Traffic Balancing Routing in Wireless Mesh Networks <sup>3</sup>

**Figure 1.** An Example of a Wireless Mesh Network.

To overcome the limitations of conventional approaches, we suggest a novel routing scheme inspired by electrostatic potential theory [12–15]. The main motivation comes from the fact that packet movements can be corresponding to electric charge behaviors governed by electrostatic potential. By constructing a virtual potential field for routing, our scheme forwards a packet following the steepest gradient direction towards any mesh gateway (a destination inside a WMN) as presented in Fig. 2. Interestingly, our scheme based on nature characteristics resembles a hybrid behavior of back-pressure and geographic routing schemes. With the help of numerical analysis techniques, our scheme operates in a distributed manner. Furthermore, our formula is equipped with a Gaussian function to adjust a routing reflecting ratio of back-pressure and geographic routing schemes for dynamic traffic environments.

**Figure 2.** An Example of Potential Field Formation for a Wireless Mesh Network.

and parameters to determine scalar values for a field.

the routing performance.

lowest gradient. Several proposed works differ by the target network, communication pattern,

Autonomous Traffi c Balancing Routing in Wireless Mesh Networks 135

A. Basu et al. have introduced potential-based routing (PB routing) [20] for unicast Internet traffic. Their idea is to set potentials with queue lengths on the top of the standard shortest path (hop count) routing. Here, the steepest gradient routing enables routers to be less congested. Even though the aim of this work is quite similar to ours, it is for fixed wired networks and unicast with flooding overheads. Regarding an anycast, V. Lenders et al. propose a density-based strategy [21] for wireless ad hoc networks in the framework of gradient-based routing. Under the scheme, a field is constructed based on node density and routing is towards a dense group destination, which increases the success probability of packet transmission. However, the routing scheme cannot react to traffic congestion; hence, even a worse scenario could occur where traffic is densely populated. For an anycast in a WMN, R. Baumann et al. develop HEAT routing [22] where a temperature field is used for routing. In this work, two metrics are considered to influence a temperature value: one is the distance from a node to a gateway, and the other is the robustness of a path towards a gateway. Because this model is based on Laplace's equation, which is a special form of Poisson's equation, it cannot deal with traffic dynamics so that congested hot spots degrade

On the other hand, our scheme utilizes the numerical analysis techniques of a finite element method (FEM) [23, 24] and a local equilibrium method (LEM) [25], to achieve a distributed algorithm [12–15]. Similarly, a finite difference method routing (FDMR) is suggested in [26] reflecting link-diversity. It is also a gradient routing scheme based on Laplace's equation.

Our work is relevant to recent approaches [17–19] motivated by physical systems of which system models have been studied for several centuries.

This chapter introduces a practical solution to develop large-scalable WMNs. The organization of this chapter is as follows. In section 2, we review relevant works and address distinguished features of our scheme. Section 3 provides a background of our work and designs a traffic-adaptive autonomous routing scheme for WMNs. In addition, we evaluate our scheme through simulations. (Section 4) Finally, we conclude this chapter in Section 5.
