A Decomposition Algorithm for Local Access Telecommunications Network Expansion Planning

Abstract

Growing demand, increasing diversity of services, and advances in transmission and switching technologies are prompting telecommunication companies to rapidly expand and modernize their networks. This paper develops and tests a decomposition methodology to generate cost-effective expansion plans, with performance guarantees, for one major component of the network hierarchy-the local access network connecting customers to the local switching center. The model captures economies of scale in facility costs, and addresses the central tradeoff between installing concentrators and expanding cables to accommodate demand growth. By exploiting the special tree and routing structure of the expansion planning problem, our solution method integrates two major algorithmic strategies from mathematical programming-the use of valid inequalities, obtained by studying a problem's polyhedral structure, and dynamic programming, which can be used to solve an uncapacitated version of the local access network expansion planning problem. The computational results for three actual test networks demonstrate that this enhanced dynamic programming algorithm, when embedded in a Lagrangian relaxation scheme (with problem preprocessing and local improvement), is very effective in generating good upper and lower bounds: implemented on a personal computer, the method was able to generate solutions that are within 1.2 to 7.0% of optimality. In addition to developing a successful solution methodology for a practical problem, this paper illustrates the possibility of effectively combining decomposition methods and polyhedral approaches.

A Tabu Search algorithm for the optimisation of telecommunication networks

“…No more sophisticated approaches have been implemented at the moment, and probably ignoring existing cable capacities does not inuence appreciably network costs in case of future very high trac demand [1]. As in [1] again, the model applies to networks where demands for different services can be expressed in commensurate units, and bandwidth/service requirements are represented only by the signalling rates allocated to the above de®ned users.…”

“…However, instead of ®nding an optimum cost network, such an approach provides solutions whose optimality depends on the approximations made. Even if accurate piecewise linear cost functions for concentrators have been introduced in [1], some authors' past experience suggests that linear programming results should be used with great caution, as the optimality with respect to the equivalent costs does not necessarily correspond to the optimality of the eective costs.…”

“…Increasing attention has been recently devoted to various problems inherent to the topological design of distributed telecommunication networks, to the Integrated Service Digital Network (ISDN) and to various problems strictly connected [1,2,4,5,14,23,25,26].…”

Combined Network Design and Multiperiod Pricing: Modeling, Solution Techniques, and Computation

“…See [1], [3], [5], [6], [8], [15], [23], [29] and the references therein. Typically, the critical decisions involve adding capacity, at minimum cost, to existing capacity levels; so that one can route known demands (fully or partly, with a penalty for shortfalls).…”

Optimizing constrained subtrees of trees

“…In treating the special case when each X i consists of all i-rooted subtrees, Barany et al(1986) describe conv(Z). In a telecommuncations study of capacity expansion for a local area network, Balakrishnan et al(1991) formulate a version of this problem as a constrained subtree packing problem and obtain practical results by tightening the formulation and using Lagrangian relaxation. Aghezzaf and Wolsey(1990) have further examined one particular aspect of their model, the question of how to correctly model a piecewise linear concave objective function.…”