Wireless Network Design: Optimization Models and Solution ...

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