Emergency Medical Service (EMS) systems can be modeled as spatially distributed queueing systems. Each location in the area has a preference ordering for the servers (usually based on proximity of calls to servers). When a call arrives, the dispatcher scans the preference list and assigns the most preferred idle vehicle to the call. If all vehicles are busy, the call is sent to a private ambulance system that operates in parallel to the EMS system. A major problem in designing and operating EMS systems is to estimate vehicle utilizations and busy probabilities for a given set of base locations. In earlier work, various systems of nonlinear equations have been proposed to estimate the vehicle utilization in EMS systems. In this paper we present a general model structure that encompasses much of the past work. We develop convergence conditions for the general model and show that a simple bisection method can be used to find solutions. The bisection method also leads to a test for the uniqueness of the solution. We demonstrate the method on a problem with 5 vehicle bases and 300 demand locations.
ASJC Scopus subject areas
- Modeling and Simulation