Wireless Network Design: Optimization Models and Solution ...

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Chapter 8 The Design of Partially Survivable Networks Syam Menon Abstract In cellular telecommunications networks, a mobile telephone switching office (MTSO) co-ordinates the activities of the mobile units either directly or through intermediate hubs. In order to increase reliability, cells often split their traffic via multiple hubs — this ensures partial survivability in the face of equipment failures. This chapter examines three related problems in the context of partial survivability. The first is a single-period model that addresses the question of assigning cells to hubs at minimum cost, while incorporating diversity requirements. The second extends the problem into a multi-period context, while the third incorporates capacity requirements at the hubs. Results from extensive computational tests are presented for the first two versions of the problem, while limited results are presented for the third. 8.1 Introduction Cellular telecommunications systems have three basic components — mobile units, base transceivers or hubs at the cell sites and the mobile telephone switching office (MTSO). The MTSO co-ordinates the activities of the base transceivers in addition to connecting calls to the wired telephone network. Calls from (or to) mobile units are routed via the base transceivers to the MTSO for processing. The mobile units connect to the transceivers via radio links while the transceivers connect to the MTSO either via microwave or via terrestrial digital lines. Readers interested in details of the components of cellular networks are referred to books in this area (e.g. Lee [11]). The number of simultaneous calls that can be handled by a cell can be expressed in terms of the number of 64 kbps DS-0 channels it needs in order to communicate Syam Menon School of Management, University of Texas at Dallas, Richardson, TX 75083, USA, e-mail: syam@utdallas.edu J. Kennington et al. (eds.), Wireless Network Design: Optimization Models and Solution Procedures, International Series in Operations Research and Management Science 158, DOI 10.1007/978-1-4419-6111-2_8, © Springer Science+Business Media, LLC 2011 177
178 Syam Menon with the MTSO. Every cell has to be connected to the MTSO, either directly or through hubs that aggregate traffic from multiple cells and connect to the MTSO via higher capacity links. With increasing size, the latter approach becomes more attractive as it enables the owner of the network to reduce costs by taking advantage of economies of scale. The increased efficiency comes with reliability concerns however, as the failure of even one high capacity line could have a significant impact on the entire network. Common approaches to tackling this issue include the use of multiple paths (Cardwell et. al. [3]) and self-healing SONET rings (e.g., Sosonsky and Wu [17]). SONET rings are particularly convenient as they provide high capacity at a reasonable cost. In addition, if the cable is severed at some point in the ring, data can re-route itself with little to no loss in information. The increased flexibility and bandwidth availability of SONET provides significant advantages over older systems. These include reduced equipment requirements, increased network reliability, and a synchronous structure which greatly simplifies the interface to digital switches and digital adddrop multiplexers. Most large companies lease transmission capacity on their SONET rings to other organizations. Dutta and Kubat [4] introduced the problem of designing partially survivable interconnect networks for a cellular system that has access to this leased capacity. They represented the problem as an integer program that minimizes the cost of transmission subject to reliability requirements and assumed a self-healing ring topology for the backbone network. They showed that the problem was NPhard and developed an efficient heuristic based on Lagrangian relaxation. This was further addressed in Menon and Amiri [13], who showed that the problem could be solved efficiently via dynamic programming. This single-period problem is the first one addressed in this chapter. Cellular telecommunications systems tend to be more flexible than traditional ones. As a result, traditional approaches to telecommunications network design are often inappropriate for the design of cellular networks, and approaches which explicitly incorporate the increased flexibility into the design process are necessary. The second problem we consider in this chapter is a multi-period model that was addressed in Kubat and Smith [8] and Menon and Amiri [14]. It exploits the flexibility of cellular systems by designing a multi-period cell-MTSO interconnection network. The objective is to minimize the total interconnection costs over the planning horizon, while determining homing decisions for the cells in each planning period. The third problem considered in this chapter was introduced by Kubat et al. [9]. In this problem, reliability requirements are incorporated in the face of capacity constraints. They represent the problem as an integer program that minimizes the cost of transmission subject to reliability requirements while assuming a tree topology for the underlying network. We introduce a new formulation for this problem and present a procedure based on column generation to solve it. Each problem is discussed in a separate section of this chapter. The single period problem is addressed in Section 8.2, while the multi-period and capacity constrained
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International Series in Operations
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Editors Jeff Kennington Eli Olinick
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vi Preface assistance. The work of
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viii Contents 3.4.1 Experiments to
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xii Contents References . . . . . .
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List of Contributors Khaldoun Al Ag
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List of Contributors xvii Nitin Sal
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Chapter 1 Introduction to Optimizat
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1 Introduction to Optimization in W
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1 Introduction to Optimization in W
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Part I Background
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26 Dinesh Rajan B(z) = 1 � (1 + z
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Part II Optimization Problems for N
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