An approximate hypercube model for public service systems with co-located servers and multiple response

Spatial queueing models help to evaluate the design of public safety systems such as fire, emergency medical service, and police departments, where vehicles are sent to geographically dispersed calls for service. We propose a new approximate hypercube spatial queueing model that allows for multiple servers to be located at the same station as well as multiple servers to be dispatched to a single call. We introduce the M[G]/M/s/s queueing model as an extension to the M/M/s/s model which allows for a single customer to request multiple servers with a general discrete probability distribution G. We use the M[G]/M/s/s queueing model to derive approximate formulas for the hypercube spatial queueing outputs. A simulation study validates the accuracy of the queueing approximations. Computational results suggest that the models are effective in evaluating the performance of emergency systems.