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Multiple Unit Dispatches in Emergency Services: Models to Estimate System Performance

Author

Listed:
  • Kenneth R. Chelst

    (Wayne State University)

  • Ziv Barlach

    (Wayne State University)

Abstract

One emergency service system model that has undergone extensive development and testing is the hypercube queuing model and its approximate analog, which were developed by Larson. The model estimates key system performance measures, such as individual unit workloads and travel times. One limitation of this model, as well as other probabilistic deployment models, is that they assume only a single unit is dispatched to each call. In the police environment, if two officers are assigned to each unit, this assumption is generally valid. However, most fire services dispatch multiple vehicles to a serious fire, and in police departments with one-officer units, a second unit will be sent to all potentially dangerous calls. The need for a new model goes beyond an interest in more accurately estimating standard performance measures when multiple units are dispatched. New models are required to predict new performance measures that are relevant only when multiple units are dispatched. For example, what are the paired travel times of the first- and second-arriving units at an emergency? How long will the first unit be exposed at a potentially dangerous situation until a backup unit arrives? Which unit most frequently arrives first at calls requiring multiple units? In this paper we build on Larson's work and present two models, one exact, the other, approximate, which can capture the simultaneous response of two identical units dispatched to a single call. We present an example from the police context to illustrate both models and compare the speed and accuracy of the approximate model to the exact one. The workload and travel time estimates of both models differ on the average by only two percent. We conclude our presentation with a brief discussion of model extensions with a focus on the analysis of a merger of police, fire and emergency medical services into a public safety service.

Suggested Citation

  • Kenneth R. Chelst & Ziv Barlach, 1981. "Multiple Unit Dispatches in Emergency Services: Models to Estimate System Performance," Management Science, INFORMS, vol. 27(12), pages 1390-1409, December.
  • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:12:p:1390-1409
    DOI: 10.1287/mnsc.27.12.1390
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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. M S Daskin & A Haghani, 1984. "Multiple Vehicle Routing and Dispatching to an Emergency Scene," Environment and Planning A, , vol. 16(10), pages 1349-1359, October.
    3. 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.
    4. Laura McLay & Maria Mayorga, 2010. "Evaluating emergency medical service performance measures," Health Care Management Science, Springer, vol. 13(2), pages 124-136, June.
    5. Mateusz Iwo Dubaniowski & Hans Rudolf Heinimann, 2021. "Time Granularity Impact on Propagation of Disruptions in a System-of-Systems Simulation of Infrastructure and Business Networks," IJERPH, MDPI, vol. 18(8), pages 1-24, April.
    6. Atkinson, J.B. & Kovalenko, I.N. & Kuznetsov, N. & Mykhalevych, K.V., 2008. "A hypercube queueing loss model with customer-dependent service rates," European Journal of Operational Research, Elsevier, vol. 191(1), pages 223-239, November.
    7. Erdemir, Elif Tokar & Batta, Rajan & Rogerson, Peter A. & Blatt, Alan & Flanigan, Marie, 2010. "Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach," European Journal of Operational Research, Elsevier, vol. 207(2), pages 736-749, December.
    8. Morabito, Reinaldo & Chiyoshi, Fernando & Galvão, Roberto D., 2008. "Non-homogeneous servers in emergency medical systems: Practical applications using the hypercube queueing model," Socio-Economic Planning Sciences, Elsevier, vol. 42(4), pages 255-270, December.
    9. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    10. Laura A. McLay & Maria E. Mayorga, 2013. "A Dispatching Model for Server-to-Customer Systems That Balances Efficiency and Equity," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 205-220, May.
    11. Geroliminis, Nikolas & Kepaptsoglou, Konstantinos & Karlaftis, Matthew G., 2011. "A hybrid hypercube - Genetic algorithm approach for deploying many emergency response mobile units in an urban network," European Journal of Operational Research, Elsevier, vol. 210(2), pages 287-300, April.
    12. de Souza, Regiane Máximo & Morabito, Reinaldo & Chiyoshi, Fernando Y. & Iannoni, Ana Paula, 2015. "Incorporating priorities for waiting customers in the hypercube queuing model with application to an emergency medical service system in Brazil," European Journal of Operational Research, Elsevier, vol. 242(1), pages 274-285.
    13. Caio Vitor Beojone & Regiane Máximo de Souza & Ana Paula Iannoni, 2021. "An Efficient Exact Hypercube Model with Fully Dedicated Servers," Transportation Science, INFORMS, vol. 55(1), pages 222-237, 1-2.
    14. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.
    15. 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.
    16. Ana Iannoni & Reinaldo Morabito & Cem Saydam, 2008. "A hypercube queueing model embedded into a genetic algorithm for ambulance deployment on highways," Annals of Operations Research, Springer, vol. 157(1), pages 207-224, January.
    17. 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).
    18. Iannoni, Ana Paula & Morabito, Reinaldo & Saydam, Cem, 2009. "An optimization approach for ambulance location and the districting of the response segments on highways," European Journal of Operational Research, Elsevier, vol. 195(2), pages 528-542, June.
    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. Shariat-Mohaymany, Afshin & Babaei, Mohsen & Moadi, Saeed & Amiripour, Sayyed Mahdi, 2012. "Linear upper-bound unavailability set covering models for locating ambulances: Application to Tehran rural roads," European Journal of Operational Research, Elsevier, vol. 221(1), pages 263-272.
    21. 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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