A general model and convergence results for determining vehicle utilization in emergency systems

Jeffrey B Goldberg, Ferenc Szidarovszky

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)137-160
Number of pages24
JournalCommunications in Statistics. Stochastic Models
Volume7
Issue number1
DOIs
StatePublished - 1991

Fingerprint

Emergency
Convergence Results
Bisection Method
Servers
Server
Ambulances
Model
Convergence Condition
System of Nonlinear Equations
Queueing System
Model structures
Nonlinear equations
Estimate
Proximity
Assign
Distributed Systems
Uniqueness
Demonstrate

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Modeling and Simulation

Cite this

A general model and convergence results for determining vehicle utilization in emergency systems. / Goldberg, Jeffrey B; Szidarovszky, Ferenc.

In: Communications in Statistics. Stochastic Models, Vol. 7, No. 1, 1991, p. 137-160.

Research output: Contribution to journalArticle

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