The multi-hour bandwidth packing problem

Abstract

We study the multi-hour bandwidth packing problem arising from telecommunications networks. The problem consists of selecting calls from a list of requests with time varying traffic conditions to be routed on an arc-capacitated network in order to maximize profit. The paper represents a significant improvement over previous research by presenting a unified model of the problem that considers all possible paths for each call and allows the traffic requirements of the calls to vary over the busy-hours of the day. Failure to consider all possible routes and to allow traffic requirements to vary over the busy-hours would lead to significant revenue loss, excessive costs and/or inferior quality of service to users. The integer programming model for the problem is presented. A solution procedure based on the Lagrangean relaxation technique is developed. The results of extensive computational experiments over a wide range of problem structures indicate that the procedure is both efficient and effective. Scope and purpose In this article we study the multi-hour bandwidth packing problem that involves selecting calls from a list of requests to be routed in a telecommunications network. The traffic requirements of the calls are allowed to vary during different periods of the day, called busy-hours. The best routes for the selected calls are generated from among all possible calls in the network. The goal of the problem is to maximize the total profit from routed calls without exceeding the capacities of the network links. Failure to allow traffic requirements to vary over the busy-hours and to consider all possible routes would lead to significant revenue loss, excessive costs and/or inferior quality of service to users. A mathematical programming formulation of the problem is presented. An efficient Lagrangean relaxation based heuristic procedure for generating feasible solutions and bounds to evaluate the quality of the solutions is developed. The results of extensive computational experiments show that the solution procedure is both efficient and effective.