Applications of maximum queue lengths to call center management

Abstract

This paper deals with the distribution of the maximum queue length in two-dimensional Markov models. In this framework, two typical assumptions are: (1) the stationary regime, and (2) the system homogeneity (i.e., homogeneity of the underlying infinitesimal generator). In the absence of these assumptions, the computation of the stationary queue length distribution becomes extremely intricate or, even, intractable. The use of maximum queue lengths provides an alternative queueing measure overcoming these problems. We apply our results to some problems arising from call center management.