Using Parallel Iteration for Approximate Analysis of a Multiple Server Queueing System

This paper describes an iterative approach to the analysis of Markovian service systems. The method is approximate unless an assumption of independence among servers is valid. Nevertheless, useful results are attainable that hold intuitive appeal and provide a geometric reduction in the number of states (hence, computation) needed to obtain solutions. We demonstrate the usefulness of the procedure through an error analysis of a simple system. The practical utility of the approach is further justified in a comparison with simulation results for a police patrol model with over 50 million states.