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A Nonlinear Programming Heuristic for Computing Optimal Link Capacities in a Multi-Hour Alternate Routing Communications Network

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  • Eric Rosenberg

    (AT&T Bell Laboratories, Holmdel, New Jersey)

Abstract

We consider the problem of determining the optimal number of communications channels in a telecommunications network. Traffic between pairs of nodes is assumed to vary with the time of day. Traffic between two nodes can flow over a one-link direct path or, if no direct channels are available, over a two-link alternate route. The problem is to compute the optimal number of channels on each link to minimize cost, subject to a constraint that enough trunks are present so that the probability of no idle channel does not exceed a specified amount. The mathematical formulation of this problem, known as the multi-hour engineering problem, yields an integer nonlinear programming problem (NLP). We apply recursive quadratic programming, with exact penalty function (EPF) line searches, to solve the continuous NLP, and use the special problem structure to provide a starting point and EPF parameter. A simple heuristic is used to obtain integral number of channels satisfying desired blocking objectives. The method successfully solved a set of randomly generated test problems with up to 35 variables and 432 nonlinear constraints.

Suggested Citation

  • Eric Rosenberg, 1987. "A Nonlinear Programming Heuristic for Computing Optimal Link Capacities in a Multi-Hour Alternate Routing Communications Network," Operations Research, INFORMS, vol. 35(3), pages 354-364, June.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:3:p:354-364
    DOI: 10.1287/opre.35.3.354
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    Cited by:

    1. Amiri, Ali & Pirkul, Hasan, 1999. "Routing and capacity assignment in backbone communication networks under time varying traffic conditions," European Journal of Operational Research, Elsevier, vol. 117(1), pages 15-29, August.

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