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 language | English (US) |
|---|---|
| Pages (from-to) | 137-160 |
| Number of pages | 24 |
| Journal | Communications in Statistics. Stochastic Models |
| Volume | 7 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1991 |
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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 journal › Article
}
TY - JOUR
T1 - A general model and convergence results for determining vehicle utilization in emergency systems
AU - Goldberg, Jeffrey B
AU - Szidarovszky, Ferenc
PY - 1991
Y1 - 1991
N2 - 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.
AB - 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.
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U2 - 10.1080/15326349108807180
DO - 10.1080/15326349108807180
M3 - Article
VL - 7
SP - 137
EP - 160
JO - Stochastic Models
JF - Stochastic Models
SN - 1532-6349
IS - 1
ER -