The stochastic queue center problem

This paper considers the Stochastic Queue Center problem, which seeks to locate a single facility with a center-type objective in an M/G/1 queue operating environment. The objective function that we consider is to minimize a positive weighted linear function of the square of the average response time and the variance of the response time to a call. The Stochastic Queue Center problem is discussed on both a discrete and a network location topology. When potential facility locations are restricted to a "nite set of discrete points, an e$cient algorithm is developed to solve for the optimal facility location parametrically in the arrival rate. By exploiting convexity properties of the objective function, we develop an e$cient "nite-step algorithm to "nd the Stochastic Queue Center on a network. The major conclusion of this work is that incorporating the variance term in the objective function has a major impact on the choice of the optimal location. We illustrate the results with an example drawn from a potential application of the model for locating an emergency transport center serving di!erent municipalities in Camden County, NJ. ( 1999 Elsevier Science Ltd. All rights reserved.