A hypercube queuing model for facility location and redistricting in urban emergency services

Larson, Richard C.

doi:10.1016/0305-0548(74)90076-8

Cited by 548 publications

(264 citation statements)

References 11 publications

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“…The main descriptive model that is relevant for our purposes is the hypercube model developed by Larson (1974) and subsequent approximate versions of that model (Larson, 1975 andJarvis, 1985). This model allows busy fractions to vary between ambulances and can accommodate ambulances responding to calls outside their assigned districts.…”

Section: Literaturementioning

confidence: 99%

“…In the original hypercube model (Larson, 1974), service times (the time an ambulance is tied up with a call) are assumed exponentially distributed. The pre-travel delay and the travel time are part of the service time and if these components are lognormally distributed then the service times will be far from exponentially distributed.…”

Section: S(x) As Computed In Formulation (P1)mentioning

confidence: 99%

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Optimal ambulance location with random delays and travel times

Ingolfsson

Budge

Erkut

2008

Health Care Manage Sci

210

102

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We describe an optimization model for ambulance location that maximizes the expected system wide coverage, given a total number of ambulances. The model measures expected coverage as the fraction of calls reached within a given time standard and considers response time to be composed of a random delay (prior to travel to the scene) plus a random travel time. Pre-travel delays at dispatch and activation stages can be significant, and models that do not account for such delays can severely overestimate the possible coverage for a given number of ambulances and underestimate the number of ambulances needed to provide a specified coverage level. By explicitly modeling the randomness in the delays and the travel time, we arrive at a more realistic model for ambulance location. In order to capture the dependence of ambulance busy fractions on the allocation of ambulances between stations, we iterate between solving the optimization model and using the approximate hypercube model to calculate busy fractions. We illustrate the use of the model using actual data from Edmonton.

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Section: Literaturementioning

confidence: 99%

Section: S(x) As Computed In Formulation (P1)mentioning

confidence: 99%

Optimal ambulance location with random delays and travel times

Ingolfsson

Budge

Erkut

2008

Health Care Manage Sci

210

102

View full text Add to dashboard Cite

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“…To Atom Atom 1 2 3 1 0 2 1 2 1 0 2 3 2 1 0 We start by considering the basic hypercube queueing model as known in the literature (Larson, 1974;Larson & Odoni, 1981). For this model, we assume that each atom is the home location of a server, and a fixed-preference dispatch policy, with preferences set according to shortest distances is in use.…”

Section: Frommentioning

confidence: 99%

“…Surveys on probabilistic location models that use mobile servers in ESS can be found, for example, in Larson & Odoni (1981), Kolesar & Swersey (1986), ReVelle (1989) Larson (1974) and extended by other authors (Swersey, 1994) is an effective descriptive model for designing and planning server-to-customer ESS. The basic idea of the model is to expand the state space description of a queueing system with multiple servers in order to represent each server individually and incorporate more complex dispatch policies.…”

Section: Introductionmentioning

confidence: 99%

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

Chiyoshi¹,

Iannoni

Morábito

2011

Pesqui. Oper.

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ABSTRACT. This paper presents some extensions and applications of hypercube queueing models to describe 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.

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Endotracheal Intubation in the Prehospital Phase of Emergency Medical Care

Jacobs¹

1983

JAMA

149

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A hypercube queuing model for facility location and redistricting in urban emergency services

Cited by 548 publications

References 11 publications

Optimal ambulance location with random delays and travel times

Optimal ambulance location with random delays and travel times

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

Endotracheal Intubation in the Prehospital Phase of Emergency Medical Care

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