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Technical Note---Approximating Vehicle Dispatch Probabilities for Emergency Service Systems with Location-Specific Service Times and Multiple Units per Location

Author

Listed:
  • Susan Budge

    (School of Business, University of Alberta, Edmonton, Alberta, Canada T6G 2R6)

  • Armann Ingolfsson

    (School of Business, University of Alberta, Edmonton, Alberta, Canada T6G 2R6)

  • Erhan Erkut

    (Ozyegin University, Istanbul, Turkey)

Abstract

To calculate many of the important performance measures for an emergency response system, one requires knowledge of the probability that a particular server will respond to an incoming call at a particular location. Estimating these “dispatch probabilities” is complicated by four important characteristics of emergency service systems. We discuss these characteristics and extend previous approximation methods for calculating dispatch probabilities to account for the possibilities of workload variation by station, multiple vehicles per station, call- and station-dependent service times, and server cooperation and dependence.

Suggested Citation

  • Susan Budge & Armann Ingolfsson & Erhan Erkut, 2009. "Technical Note---Approximating Vehicle Dispatch Probabilities for Emergency Service Systems with Location-Specific Service Times and Multiple Units per Location," Operations Research, INFORMS, vol. 57(1), pages 251-255, February.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:1:p:251-255
    DOI: 10.1287/opre.1080.0591
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    References listed on IDEAS

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    1. Richard C. Larson, 1975. "Approximating the Performance of Urban Emergency Service Systems," Operations Research, INFORMS, vol. 23(5), pages 845-868, October.
    2. J. P. Jarvis, 1985. "Approximating the Equilibrium Behavior of Multi-Server Loss Systems," Management Science, INFORMS, vol. 31(2), pages 235-239, February.
    3. Jeffrey Goldberg & Ferenc Szidarovszky, 1991. "Methods for Solving Nonlinear Equations Used in Evaluating Emergency Vehicle Busy Probabilities," Operations Research, INFORMS, vol. 39(6), pages 903-916, December.
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    Cited by:

    1. Iannoni, Ana Paula & Chiyoshi, Fernando & Morabito, Reinaldo, 2015. "A spatially distributed queuing model considering dispatching policies with server reservation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 49-66.
    2. Kevin Taaffe & Yann B. Ferrand & Amin Khoshkenar & Lawrence Fredendall & Dee San & Patrick Rosopa & Anjali Joseph, 2023. "Operating room design using agent-based simulation to reduce room obstructions," Health Care Management Science, Springer, vol. 26(2), pages 261-278, June.
    3. Susana Baptista & Rui Oliveira, 2012. "A case study on the application of an approximated hypercube model to emergency medical systems management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 559-581, December.
    4. Rautenstrauss, Maximiliane & Martin, Layla & Minner, Stefan, 2023. "Ambulance dispatching during a pandemic: Tradeoffs of categorizing patients and allocating ambulances," European Journal of Operational Research, Elsevier, vol. 304(1), pages 239-254.
    5. Kenneth C. Chong & Shane G. Henderson & Mark E. Lewis, 2016. "The Vehicle Mix Decision in Emergency Medical Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 347-360, July.
    6. Hyunjin Lee & Taesik Lee, 2021. "Demand modelling for emergency medical service system with multiple casualties cases: k-inflated mixture regression model," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 1090-1115, December.
    7. Knight, V.A. & Harper, P.R. & Smith, L., 2012. "Ambulance allocation for maximal survival with heterogeneous outcome measures," Omega, Elsevier, vol. 40(6), pages 918-926.
    8. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    9. Boyacı, Burak & Geroliminis, Nikolas, 2015. "Approximation methods for large-scale spatial queueing systems," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 151-181.
    10. Iannoni, Ana Paula & Morabito, Reinaldo & Saydam, Cem, 2011. "Optimizing large-scale emergency medical system operations on highways using the hypercube queuing model," Socio-Economic Planning Sciences, Elsevier, vol. 45(3), pages 105-117, September.
    11. Iannoni, Ana P. & Morabito, Reinaldo, 2023. "A review on hypercube queuing model's extensions for practical applications," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    12. Akbar Karimi & Michel Gendreau & Vedat Verter, 2018. "Performance Approximation of Emergency Service Systems with Priorities and Partial Backups," Transportation Science, INFORMS, vol. 52(5), pages 1235-1252, October.
    13. Akdogan, M. Altan & Bayındır, Z. Pelin & Iyigun, Cem, 2023. "An analysis of ambulance location problem from an equity perspective," Socio-Economic Planning Sciences, Elsevier, vol. 90(C).
    14. Soovin Yoon & Laura A. Albert, 2018. "An expected coverage model with a cutoff priority queue," Health Care Management Science, Springer, vol. 21(4), pages 517-533, December.
    15. Bélanger, V. & Lanzarone, E. & Nicoletta, V. & Ruiz, A. & Soriano, P., 2020. "A recursive simulation-optimization framework for the ambulance location and dispatching problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 713-725.
    16. Yoon, Soovin & Albert, Laura A., 2021. "Dynamic dispatch policies for emergency response with multiple types of vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    17. Susan Budge & Armann Ingolfsson & Dawit Zerom, 2010. "Empirical Analysis of Ambulance Travel Times: The Case of Calgary Emergency Medical Services," Management Science, INFORMS, vol. 56(4), pages 716-723, April.
    18. Yoon, Soovin & Albert, Laura A., 2020. "A dynamic ambulance routing model with multiple response," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    19. Ansari, Sardar & Yoon, Soovin & Albert, Laura A., 2017. "An approximate hypercube model for public service systems with co-located servers and multiple response," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 143-157.
    20. Sardar Ansari & Laura Albert McLay & Maria E. Mayorga, 2017. "A Maximum Expected Covering Problem for District Design," Transportation Science, INFORMS, vol. 51(1), pages 376-390, February.

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