A mathematical formulation for joint channel assignment and multicast routing in multi-channel multi-radio wireless mesh networks

Abstract

Multicast routing is generally an efficient mechanism for delivering identical content to a group of receivers. Multicast is also deemed a key enabling service for a wealth of audio and video applications as well as data dissemination protocols over the last-mile backhaul Internet connectivity provided by multi-channel multi-radio wireless mesh networks (MCMR WMNs). Major prior art multicast protocols in these networks center around heuristic or meta-heuristic initiatives in which channel assignment and multicast routing are considered as two separate sub-problems to be solved in sequence. It might even be the cast that the solution for either of these two sub-problems is assumed to be preparatively calculated and given as input to the other. Within this perspective, however, the interplay between the two sub-problems would essentially be ruled out from the computations, resulting in sub-optimal solutions for network configuration. The work in this article is targeted at promoting the adoption of cross-layer design for joint channel assignment and multicast tree construction problem in MCMR WMNs. In the proposed scheme, contrary to the existing methods, these two sub-problems will be solved conjointly and an optimal solution is provided. In particular, a comprehensive cross-optimization framework based on the binary integer programming (BIP) formulation of the problem is presented which also addresses the hidden channel problem in MCMR WMNs. We have, as well, conducted an extensive series of simulation experiments to verify the efficacy of the proposed method. Also, experimental results demonstrate that the proposed method outperforms the genetic algorithm and the simulated annealing based methods proposed by Cheng and Yang (2011) in terms of interference.

Introduction

Wireless mesh network (WMN) is an emerging technology primarily aimed at provisioning for wireless Internet access and scalable QoS-aware delivery of heterogeneous traffic over an integrated milieu of both ad-hoc and infrastructure operation modes (Akyildiz and Wang, 2005, Martínez and Bafalluy, 2010). A typical deployment of a WMN is comprised of three layers: the highest layer consists of one or more gateways, also referred to as mesh portals, which connects the WMN to wireline Internet and enables the traffic exchange in between the two networks. The middle layer, however, features the mesh routers which form the WMN’s backbone and are in charge of managing the traffic flow across the mesh setting. The nodes located at the lowest layer are essentially the network users (mesh clients in WMN’s parlance) with limited capability. This level may also consist of several WLANs or cellular networks. Contrary to mobile ad-hoc networks (MANETs), the wireless mesh backbone is usually stationary, and as opposed to wireless sensor networks (WSNs), there is no limitation on the nodes’ power consumption. An indispensible concern in WMNs, however, is to boost the physical layer capacity and to reduce interference, which is normally achieved by equipping each node with a limited number of radios, usually less than or equal to the number of available channels (Ma et al., 2008, Baul et al., 2004). Each node would then be able to transmit and receive data simultaneously through different channels (Gupta and Kumar, 2000; Das et al., 2006; Xu, 2006). Wireless mesh networks operating with multiple channels on multiple radio interfaces are henceforth referred to in this article as MCMR WMNs.

Of the niche areas of application in the context of MCMR WMNs are multicast-based systems such as video conferencing, online games, webcast and distance learning, to name a few. While wireless communication is intrinsically apt for performing multicast routing due to the broadcast nature of the air medium, the inter-channel interference in WMNs plays a key factor in determining the actual data rate achievable for a multicast service. The issue of interference reduction in MCMR WMNs is typically dealt with by developing a channel assignment strategy which effectively specifies the most appropriate channel-radio associations. However, channel assignment brings about its own complications; in effect, an additional constraint ought to be satisfied for network connectivity in MCMR WMNs as compared to the conventional wireless networks; more specifically, two nodes are considered neighbors only if: (1) they are located within the transmission range of each other and; (2) there exists a common channel assigned to the radios of both nodes. This second constraint essentially complicates the multicast routing problem in that the multicast tree construction should necessarily be performed in accord with channel-radio associations such that the overall interference in the network is kept at minimum. The channel assignment problem has previously been investigated in the context of unicast routing by many researchers (e.g. Skalli et al., 2007, Subramanian et al., 2007, Mohsenian and Wong, 2006, Ramachandran et al., 2006, Marina and Das, 2005, Das et al., 2005, Alicherry et al., 2005, Tang et al., 2005, Raniwala et al., 2004, Tasaki et al., 2004, Kodialam and Nandagopal, 2005); unicast-based interference reduction schemes can, in essence, be classified along the lines of the following two categories:

• Disjoint

  • channel assignment on a given routing topology (Mohsenian and Wong, 2006, Das et al., 2005, Raniwala et al., 2004)

  • routing over a given channel assignment scheme (Subramanian et al., 2007, Ramachandran et al., 2006, Marina and Das, 2005, Tang et al., 2005)

• Joint channel assignment and routing (Alicherry et al., 2005, Kodialam and Nandagopal, 2005)

Obviously, unicast-based implementations are not readily applicable or at least scalable enough to be employed in the one-to-many paradigm of a typical multicast communications setting. Moreover, given the bandwidth-constrained operation of wireless networks, the existing wireline multicast solutions cannot be ported to mesh systems without fundamentally changing their behavior to reduce overhead. Multicasting in MANETs and WSNs also address route recovery and energy concerns, respectively, which are characteristically different from the pivotal issues of throughput and interference raised in the middle layer of MCMR WMNs. Routing in these networks is further complicated given that the multiple radios on each node may dynamically switch on different channels. WMN-based multicasting has been discussed in Keegan et al. (2008), Ruiz and Gomez-Skarmeta (2005), Roy et al. (2008), Zhao et al. (2006), Yuan et al. (2006), Shittu et al. (2008), Ruiz et al. (2006), Akyildiz and Wang (2008)and Palomar and Chiang (2006), albeit for single channel single radio scenarios, as well as in Karimi et al. (2010) for multi-channel single radio settings, which characterize significantly different network configurations and thus lie outside the scope of this paper.

Fig. 1 depicts an example of the joint multicast tree construction and channel assignment problem in an MCMR WMN. The node ‘MS’ (i.e. multicast source) sends the same data to multicast targets which happen to be connected to different networks at the lowest layer of the mesh hierarchy. MT1 through MT4might, for instance, be laptops, cell phones, PDAs, or even a sensor node. The numbers printed next to the links denote the channel-radio associations. Despite its vast number of applications and practical importance, few works have specifically been targeted at multicast performance optimization in MCMR WMNs. The mainstream of research in this area has considered the channel assignment and multicast routing as two disjoint sub-problems to be solved in sequence (Zeng et al., 2007, Zeng et al., 2010, Cheng and Yang, 2008a, Cheng and Yang, 2008b, Cheng and Yang, 2011, Lim et al., 2009); as envisaged in Nguyen and Nguyen, 2008, Nguyen and Nguyen, 2009a, Nguyen and Nguyen, 2009b and Yin et al. (2007), it might even be the cast that the solution for either of these two sub-problems is assumed to be preparatively calculated and given as input to the other. The downside associated with these schemes, however, is that the cross-interaction between the two sub-problems would not be accounted for and that their reliance on heuristic or meta-heuristic initiatives does not come up with the optimal solution.

In general, practical network-driven application scenarios call for proper mathematical formulations of the underlying logic to ensure the optimality of the resultant configurations and of the choices made for performance tuning parameters. To the best of our knowledge, no previous study has explored the mathematical formulation for the joint channel assignment and multicast tree construction problem in MCMR WMNs. Therefore, in this article, for the first time, we present a cross-layer optimization framework for the joint channel assignment and multicast tree construction problem. In comparison with the existing schemes, the two sub-problems would be solved conjointly and their impact on each other will be thoroughly examined. Our proposed framework is based on binary integer programming (BIP) which is particularly interesting given its specific capability in fully utilizing a larger pool of available resources (viz. channels and/or radios) in order to come up with the most efficient assignment scheme necessary for multicast routing interference minimization. Moreover, the solution resultant from a BIP formulation of the problem basically serves as a yardstick for performance evaluation of comparable centralized and/or distributed methods.

Given the relatively limited scale of typical WMN deployments and their arguably low density (Nguyen and Xu, 2007, Nguyen, 2008), a BIP-based formulation would prove a reasonable choice. BIP models also exhibit appropriate degrees of flexibility in that in many cases we might be able to extend the problem definition with new constraints simply via adding new variables and inequalities. Our proposed model also accounts for the hidden channel problem (Lim et al., 2009), which typically occurs when two-hop away nodes attempt to tune on the same channel. Finally, we demonstrate the efficacy of our approach through an extensive set of experimental evaluations.

The reminder of this paper is organized as follows: In Section 2, we survey the prior art multicast methods in MCMR WMNs and would highlight their advantages as well as the associated performance issues. Our mathematical formulation for the cross-optimization of the joint channel assignment and multicast routing problem will be presented in Section 3. In Section 4, we examine the correctness of our approach with respect to connectivity and loop occurrence and will also discuss the outcome of several performance measurement studies. Section 5 concludes the article.