Gateway selection and routing in wireless mesh networks

doi:10.1016/j.comnet.2009.04.017

Computer Networks

Volume 54, Issue 2, 15 February 2010, Pages 319-329

https://doi.org/10.1016/j.comnet.2009.04.017 Get rights and content

Abstract

This paper deals with issues regarding network planning and optimization in multi-hop wireless mesh networks (WMNs). The central focus is on mathematical programming formulations for both the uncapacitated and capacitated joint gateway selection and routing (U/C-GSR) problem in WMNs, which are in general $NP$ -complete, when expressed as decision problems. We detail a reformulation using the shortest path cost matrix (SPM) and prove that it gives the optimal solution when applied to the uncapacitated case. We extend the SPM formulation to the capacitated case and show computationally, by using a lower bound on the optimal solution, that it performs within a small optimality gap. Evidence from numerical investigations shows that, the proposed formulation can dramatically improve the computation time for WMNs with realistic network sizes. Furthermore, a set of extensions to the basic formulation is detailed to allow modeling issues such as multi-rate transmission, restricting the number of hops in each routing sub-tree and declaring unreliable nodes as leaf nodes in the routing tree.

Introduction

Undoubtedly wireless mesh networks (WMNs) have recently received significant research attention both from academia and industry. In large part this interest stems from the fact that WMNs can fulfill a wide set of different operational roles. These roles can range from last mile broadband connectivity for un-tethered Internet access at home and in the office, to backhaul support in 2.5/3G and emerging cellular networks.

In WMNs, nodes are connected to a pre-defined set of gateways nodes through wireless multi-hop transmission. The key role of the gateways is to provide wide area connectivity for all nodes in the network. One of the most promising emerging technologies for deploying WMNs is the IEEE 802.16 standard, which has been approved and published in 2002, but since then several amendments have been introduced [1], [2]. In parallel to the standardization activities, a significant number of WMNs are currently planned, are in a pre-deployment (testing) phase or have already being deployed. Along these lines it is worth mentioning the efforts in [3], [4], [5], [6].

In practice, large scale wireless multi-hop mesh networks will rarely involve a single gateway (i.e., a root node that provides connectivity to the global Internet for all nodes in the mesh network). In that respect, by allowing multiple gateway nodes to be deployed in the network and allowing flexibility in their selection, a number of fundamental intertwined design aspects emerge: (i) the gateway selection, (ii) the assignments of nodes to gateways and (iii) the routing paths through wireless multi-hop transmission from the selected gateways to the nodes. With respect to the routing, we note that we have placed our emphasis on tree construction rather than general multi-path routing because centralized or distributed scheduling in trees is supported within the IEEE 802.16 standard. Therefore, efficient spanning tree construction becomes a key aspect for efficient WMN deployment. A pictorial representation of such a scenario is shown in Fig. 1, where two different possible layouts for the same WMN (in terms of the location of the nodes) are depicted.

Since all traffic (both uplink and downlink) flows through the gateway nodes, the spanning tree is capacity limited and therefore the number of nodes connected is inevitably limited by the capabilities of the gateway nodes. Assuming a pre-defined cost for placing root nodes there is a trade-off between how many of them will be used and the satisfiability of Quality of Service (QoS) of all participating nodes in the network. Thus, the problem is to find the minimum number of root nodes such that each node in the network can be assigned to a root node while at the same time the QoS requirement is satisfied (in terms of Kbps for example).

In this paper we focus on the problem where the number of gateways, M, to be deployed is pre-decided (i.e., there is an available budget which can be translated to a number of gateways) and the problem is to select M gateways from a set of nodes so that some performance metrics are optimized. We consider the case where flows are rooted from the gateway nodes to each node in the WMN (downlink case). The results of this paper can be extended to the case where flows are routed from each node to the gateways (uplink case).

The above described gateway selection problem closely resembles the general Facility Location Problem (FLP) [11], [12], [13]. In FLPs a number of service facilities need to be opened to serve a spatiality distributed set of customers with the minimum transportation cost. Further, when the number of facilities p to be opened is fixed, the problem is called the p-median problem. However, in the classical FLPs customers are directly connected to the facilities as opposed to our problem where nodes are connected to gateways through other nodes. The FLP has found a significant number of applications and has occupied a central place in the fields of operational research and discrete mathematics. The two main families of problems within the discrete location theory are the uncapacitated and capacitated versions of the FLP. In the latter case a restriction is imposed on the number of nodes that can be connected to a gateway; this constraint expresses the capacity of the gateway. In this paper mathematical programming formulations will be detailed for both the Uncapacitated-GSR (U-GSR) problem and the Capacitated-GSR (C-GSR) problem.

The rest of the paper is organized as follows: In Section 2 we detail closely related previous work and lineup the main contributions of the paper. Section 3 specifies the system model that has been adopted, describes the problem and details a mixed integer linear program formulation for the uncapacitated routing and gateway selection problem. In Section 4 we provide a reformulation of the problem using the all-pairs shortest path matrix. Multi-rate support and further extensions are described in Section 5. Numerical investigations are reported in Section 6 and the paper concludes in Section 7.

Section snippets

Selected previous works and research contribution

Much of recent research in WMNs has focused on advanced routing schemes that can also take interference into account [7], [8], scheduling algorithms that maximize time slot reuse [9] or optimize channel assignment [10]. Recently a number of works have touched upon the issue of gateway placement/selection and associated routing in wireless multi-hop mesh networks [14], [15], [16]. In [14] a mathematical programming formulation is discussed with a bi-objective function of minimizing the number of

Preliminaries and problem definition

A static multi-hop wireless mesh network is considered, which is represented as a directed graph $G (V, L)$ , with $V$ representing the set of nodes and $L \subseteq V \times V$ the set of links. We denote by $R \subseteq V$ the set of candidate gateway nodes and we let $M < | R |$ to be the number of gateways that will be deployed. The aim is to assign each node to a single gateway and route its demand through nodes that are also assigned to the same gateway. Hence, the U-GSR problem is defined as follows: Given a graph $G (V, L)$ , a link

Reformulation of the GSR problem based on the shortest path matrix

In this section we provide a reformulation of the GSR problem and we treat the uncapacitated and capacitated cases separately.

Multi-rate support in the SPM formulation

Up to now, we assumed that all nodes have the same capacity and hence the only required constraint was the one imposed at the gateway. However, in the case where transmitting nodes utilize adaptive modulation and coding (AMC) (this is the case for example in IEEE 802.16-2004 standard), links have different capacities depending on the distance between the transmitting and receiving pair. In this case, the transmission region can be decomposed into different regions as shown in Fig. 4, where the

Numerical investigations

We conduct numerical simulations on randomly deployed WMNs, confined in a 3 × 3 km² area with variable number of nodes $| V |$ , number of candidate gateways $R = | R |$ , and number of gateways M that need to be deployed. The following simple path loss model has been used (the results are independent of the particular path loss model used, hence more elaborate path loss models can also be applied), $PL (d) = PL (d_{o}) + 10 β \log_{10} (d / d_{o})$ where d is the distance between transmitter and receiver, $PL (d_{o})$ is the free space

Concluding remarks

In this paper we provide mathematical programming formulations for the problem of joint routing and gateway selection in wireless mesh networks. The baseline mathematical programming formulation (C-GSR) can only handle network instances of up to 22 nodes in a reasonable time (i.e., less than 2000 s). Our proposed reformulation manages to solve instances of up to 500 nodes optimally in the uncapacitated case, and with small optimality gaps in the capacitated case, in competitive computational

References (17)

Carl Eklund et al.
IEEE standard 802.16: a technical overview of the WirelessMAN air interface for broadband wireless access
IEEE Communication Magazine
(2002)
IEEE Std 802.16a-2003: IEEE Standard for Local and metropolitan area networks – Part 16: Air Interface for Fixed...
MIT Roofnet Project,...
SeattleWireless, Community Wireless Network project,...
CUWiNware Wireless Network at Champaign-Urbana,...
Self Organizing Wireless Mesh Networks,...
Richard Draves, Jitendra Padhye, Brian Zill, Routing in multi-radio, multi-hop wireless mesh networks, in:...
Douglas De Couto, Daniel Aguayo, John Bicket, Robert Morris, a high-throughput path metric for multi-hop wireless...

There are more references available in the full text version of this article.

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Katerina Papadaki graduated from the University of California at Berkeley, with a double major in Pure Mathematics and Statistics in 1994. She completed the M.Sc. in Operational Research at the London School of Economics in Operational Research in 1996. She completed her Ph.D. at Princeton University (2001) in the Department of Operations Research and Financial Engineering, where she developed approximate dynamic programming algorithms for transportation problems. She is currently a Lecturer at the Operational Research Department at London School of Economics (since 2002). Her research interest are resource allocation problems in wireless telecommunications. She is a member of the Institute for Operations Research and the Management Sciences, the Institution of Engineering and Technology and the Operational Research Society.

Vasilis Friderikos graduated from the Aristotle University of Thessaloniki, Greece, Department of Electrical and Computer Engineering, with major in Telecommunications, in 1998. He completed the M.Sc. by Research in Telecommunications (with Distinction) at the Centre for Telecommunications Research (London) in 1999. During his Ph.D. he was working as a Research Associate in Mobile-VCE Core-2 research programme on algorithmic aspects of QoS enabled pure IP based mobile/wireless networks. He has been awarded a summer research fellowships at British Telecom Laboratories in 2005 for conducting research in the area of wireless multi-hop mesh networks. He has also been seconded at the Wireless Information Network Laboratory (WINLAB) at Rutgers University, New Jersey as a visiting researcher in winter 2005. He is currently a Lecturer at King’s College London and his research interests revolve around cross layer optimization algorithms with emphasis on scheduling for single or multi-hop wireless packet transmission. He is currently co-investigator and work package leader in the EPSRC Delivery Efficiency research project and also a co-investigator in the EC-FP6 ICT Creating Ubiquitous Intelligent Sensing Environments (CRUISE) Network of Excellence (NoE) project. He is also an Alumni Business Fellow of the London Technology Network (www.ltnetwork.org) representing the Department of Electronic Engineering at various LTN events. He is a member of the Institute of Electronics and Electrical Engineers, the Institution of Engineering and Technology and the Institute for Operations Research and the Management Sciences Technical Section on Telecommunications.

^☆: A short version of this manuscript appeared previously at the IEEE Wireless Communications and Networking Conference (WCNC), Las Vegas, Nevada, USA, 31 March – 1 April, 2008, entitled Joint Routing and Gateway Selection in Wireless Mesh Networks.

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Gateway selection and routing in wireless mesh networks☆