Elsevier

Information Sciences

Volume 294, 10 February 2015, Pages 216-226
Information Sciences

To converge more quickly and effectively—Mean field annealing based optimal path selection in WMN

https://doi.org/10.1016/j.ins.2014.10.001Get rights and content

Abstract

Multi-constrained path selection with optimization aims at finding an optimal path that satisfies a set of QoS parameters, as an NP-hard problem, which is also a big challenge for wireless mesh networks. Heuristic algorithms with polynomial and pseudo-polynomial-time complexities are often used to deal with this problem. However, existing methods either have analyses in specific network models or cannot support the change of network topology well. Thus, multi-constrained QoSR in emerging wireless mesh networking is worth investigating further. In this paper, we propose a novel Routing Algorithm based on Mean Field Annealing (MFA_RA) to solve this problem. MFA_RA first uses a function of two QoS parameters, wireless link’s delay and transmission success rate, as the cost function, and then seeks to find a feasible path by mean field annealing. Moreover, a set of deterministic equations are utilized to replace the stochastic process in simulated annealing (SA), and a saddle point approximation is adopted for the calculation of the stationary probability distribution at equilibrium. Extensive simulation results demonstrate that MFA_RA is an effective algorithm and can outperform other heuristic algorithms.

Introduction

In the last few years, many research works have focused on multi-hop ad hoc networks, in which relaying nodes are in general mobile, and communication needs are primarily between nodes within the same network. However, this type of network does not yet have an impact on our way of using wireless networks. Indeed, wireless mesh network (WMN) [5], [15], a new broadband Internet access technology, which is an alias of wireless ad hoc network in the industry, is drawing significant attention these days and has been focused on by an increasing number of multi-hop wireless deployments and proprietary commercial solutions. Different from ad hoc network, WMN introduces a hierarchy in the network architecture with the implementation of dedicated nodes communicating among each other and providing wireless transport services to data traveling from users to either other users or access points (access points are special wireless routers with a high-bandwidth wired connection with the Internet backbone). In this class of networks, rather than involving pairs of terminal nodes, mostly involve communication to and from wired gateways. Numerous challenges must be overcome to realize the practical benefits of wireless mesh networking. These include high network capacity, service of differentiation support, and secure and reliable communication, and, of principal interest here, quality of service (QoS) routing issues are critical topics for WMNs. Cost-effective resolution to these issues at appropriate levels is essential for widespread general use of wireless mesh networking.

Now most QoS-sensitive applications that attract interest for use in current wired networks would attract interest for wireless mesh networks as well, therefore, providing QoS guarantees is a critical issue for wireless mesh networks and needs to be overcome to realize the practical benefits of wireless mesh networking.

More than one QoS constraint (with or without optimization) often makes the QoS routing (QoSR) problem NP-hard [14]. On one hand, due to the scarce resources and the characters of wireless communication environment, most of the current research on QoS routing in multi-hop ad hoc networks only focus on one single metric, such as delay or hop-count, and deal with the best-effort data traffic [12], [19], only few literatures take the multi-constrained QoS routing into consideration (see Section 2); on the other hand, in wired networks QoS routing has attracted much attention from both academia and industry and representative protocols such as MPLS [8], TRIP [26] and other several schemes (see Section 2) has been provided. However, these complicated protocols either have analyses in specific network models or cannot suit for WMNs with dynamically changing network topology well. Thus, the research on the multi-constrained QoSR in emerging wireless mesh networking is still insufficient.

In this paper, we propose a novel routing scheme based on MFA for multi-constrained routing in WMNs. Specifically, the main contributions of this paper are as follows.

  • (1)

    We first map the multi-constrained QoSR problem in wireless mesh networks onto the mean field network (MFN).

  • (2)

    Then a novel mean field annealing based multi-constrained routing algorithm named MFA_RA is proposed. In the proposed algorithm, we utilize a set of deterministic equations to replace the stochastic process in SA to let the annealing be more efficient.

  • (3)

    We demonstrate the performance of MFA_RA through extensive experiments. Experimental results verify that MFA_RA can find the comparable solutions more quickly than related schemes, and it is a promising multi-constraints QoS routing algorithm with optimization for wireless mesh networks.

The remainder of this paper is organized as follows. In Section 2, related work is discussed in detail. In Section 3, we give the description of the problem and the proposed algorithm. Performance evaluation for the related algorithm is presented in Section 4. Finally, we conclude this paper in Section 5 with a summary and discussion of future work.

Section snippets

Related work

There have been extensive studies on the QoS routing problem in wired or wireless networks [10], [12], [17], [19], [27], [29], [30]. With the bursting of real-time services, such as online multimedia conference and online video game in networks, multi-constrained QoS routing is playing an more and more important role in providing QoS guarantee for service flows with multiple QoS parameters, whose function is to find a feasible path that satisfies multiple constraints. Due to the NP hardness of

Pertinent information

Definition

A graph, G = (V, Γ) is used to describe a wireless mesh network with a finite non-empty node set V and a link set Γ. Each member in the link set Γ has two endpoints that can communicate with each other directly. In QoSR with optimization, each link (i, j)  Γ is associated with a primary cost parameter c(i, j) and an m-dimension additive QoS parameters vector w(i, j) = (w1(i, j), w2(i, j),  , wl(i, j),  , wm(i, j)), which is also called QoS metric w(e). Here all parameters are non-negative. Given m-dimension

Performance evaluation

We have carried out many simulations in different scenarios. Wireless mesh networks with different number nodes (routes) (i.e., 10 (36), 20 (725), 30 (11375)) are considered. The performance achieved by MFA_RA is compared to the scheme based on SA proposed in [20] because it shows SA based scheme outperformed other pertinent algorithms there. Moreover, we also compare MFA_RA with other two effective popular techniques, particle swarm optimization (PSO) [25] based scheme and ant colony

Conclusion

Searching for the optimal route that can satisfy more than one QoS parameter simultaneously in wireless mesh networks is an NP-hard combinatorial optimization problem. In this paper, a novel multi-constrained routing scheme named MFA_RA using mean field annealing is proposed. Mean field annealing, which adopts the saddle point approximation, uses a set of deterministic equations to replace the stochastic process in SA. Extensive simulation results show it can converge more quickly and escape

Acknowledgements

This work is supported partially by the national Natural Science Foundation of China (NSFC) under Grant No. 61002016, Zhejiang Provincial Natural Science Foundation of China under Grant No. LY13F010016, Qianjiang Talent Project of Zhejiang Province under Grant No. QJD1302014. The authors would like to thank the anonymous reviewers and Professor Witold Pedrycz for their helpful comments.

Lianggui Liu, Ph.D. He got the Ph.D degree in communications engineering from Nanjing University of Posts & Telecommunications, Nanjing, China, in 2007. He is now an associate professor with the School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China. He has published more than 30 research papers on communications networks in various prestigious international journals or academic conferences. Professor Liu’s research works focus on wireless mesh

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    Lianggui Liu, Ph.D. He got the Ph.D degree in communications engineering from Nanjing University of Posts & Telecommunications, Nanjing, China, in 2007. He is now an associate professor with the School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China. He has published more than 30 research papers on communications networks in various prestigious international journals or academic conferences. Professor Liu’s research works focus on wireless mesh networks, opportunistic networks, mobile ad hoc networks, network security and natural computation.

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    Weiqiang Xu, Ph.D. He got the Ph.D degree in communications engineering from Zhejiang University, Hangzhou, China, in 2006. He is now an associate professor with the School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China. His research interest includes wireless sensor networks, mobile ad hoc networks.

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