A tutorial on hypercube queueing models and some practical applications in Emergency Service Systems

Abstract

This paper presents some extensions and applications of hypercube queueing models todescribe server-to-customer type Emergency Service Systems. The classical hypercube is a well-known spatially distributed queueing model effective in analyzing these systems, based on Markovian analysis approximations. Experience has shown that each real life Emergency Service System may have its own unique characteristics so that each system may require a particular hypercube queueing model incorporating those characteristics. Some of these distinctive characteristics are considered in the extensions presented in this tutorial such as dispatch policy based on random selection of the server to take an incoming call; partial cooperation among servers whereby depending on where the call is coming from, some servers cannot take the call; servers with additional workload coming from walk-in nonemergency customers such as in customer-to-server systems; existence of calls requiring the dispatch of more than one server; existence of more than one type of servers in the system, for instance paramedical and medical units in emergency medical systems. In this study, we present a set of these models based on the smallest non-trivial service systems. For each model, the construction of the system of equations for equilibrium hypercube state probabilities and the evaluation of particular operational characteristics are described.