A mixed integer/linear programming approach to communication network design

Abstract

Optimal network design constructs network topologies that minimize total network cost while allocating capacity and routing traffic to accommodate demand and performance requirements. Such problems are characterized by large dimensionality even when relatively small networks are considered. This work revisits discrete linear approaches and describes a network design model based on a Mixed Integer/Linear Programming (MILP) formulation that does not, as most other approaches, separate the link capacity assignment from routing and topological design but fully integrates these processes. An objective of the model is to achieve balanced network designs based on uniform utilization of resources. Performance requirements lead to the incorporation into the model of lower bound on link flows and restrictions on the maximum number of hops per route. The approach is general and can be applied to packet- and circuit-switched communication networks in the presence of upper bounds on capacity allocation. Numerical results based on the solution of an MILP problem using a standard package are presented here. A numerical solution of an exact small network problem is described and compared with heuristic techniques for reducing the MILP problem size, techniques which contribute to the solution of small- and medium-sized networks. To demonstrate the flexibility and broad coverage of this basic network design model, extensions in the area of traffic and trunk routing, as well as facility design and engineering, are presented.