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A Markovian queueing model for ambulance offload delays

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  • Almehdawe, Eman
  • Jewkes, Beth
  • He, Qi-Ming

Abstract

Ambulance offload delays are a growing concern for health care providers in many countries. Offload delays occur when ambulance paramedics arriving at a hospital Emergency Department (ED) cannot transfer patient care to staff in the ED immediately. This is typically caused by overcrowding in the ED. Using queueing theory, we model the interface between a regional Emergency Medical Services (EMS) provider and multiple EDs that serve both ambulance and walk-in patients. We introduce Markov chain models for the system and solve for the steady state probability distributions of queue lengths and waiting times using matrix-analytic methods. We develop several algorithms for computing performance measures for the system, particularly the offload delays for ambulance patients. Using these algorithms, we analyze several three-hospital systems and assess the impact of system resources on offload delays. In addition, simulation is used to validate model assumptions.

Suggested Citation

  • Almehdawe, Eman & Jewkes, Beth & He, Qi-Ming, 2013. "A Markovian queueing model for ambulance offload delays," European Journal of Operational Research, Elsevier, vol. 226(3), pages 602-614.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:3:p:602-614
    DOI: 10.1016/j.ejor.2012.11.030
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    References listed on IDEAS

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    Cited by:

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    2. Leo, Gianmaria & Lodi, Andrea & Tubertini, Paolo & Di Martino, Mirko, 2016. "Emergency Department Management in Lazio, Italy," Omega, Elsevier, vol. 58(C), pages 128-138.
    3. Shovan Chowdhury, 2019. "On the Estimation of Performance Measures in a Single M/Ek/1 Queue," Working papers 301, Indian Institute of Management Kozhikode.
    4. Na Li & Nan Kong & Quanlin Li & Zhibin Jiang, 2017. "Evaluation of reverse referral partnership in a tiered hospital system – A queuing-based approach," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5647-5663, October.
    5. Golmohammadi, Davood, 2016. "Predicting hospital admissions to reduce emergency department boarding," International Journal of Production Economics, Elsevier, vol. 182(C), pages 535-544.
    6. Acuna, Jorge A. & Zayas-Castro, José L. & Charkhgard, Hadi, 2020. "Ambulance allocation optimization model for the overcrowding problem in US emergency departments: A case study in Florida," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    7. Shuwan Zhu & Wenjuan Fan & Xueping Li & Shanlin Yang, 2023. "Ambulance dispatching and operating room scheduling considering reusable resources in mass-casualty incidents," Operational Research, Springer, vol. 23(2), pages 1-37, June.
    8. Amir Rastpour & Armann Ingolfsson & Bora Kolfal, 2020. "Modeling Yellow and Red Alert Durations for Ambulance Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(8), pages 1972-1991, August.
    9. Almehdawe, Eman & Jewkes, Beth & He, Qi-Ming, 2016. "Analysis and optimization of an ambulance offload delay and allocation problem," Omega, Elsevier, vol. 65(C), pages 148-158.
    10. Li, Mengyu & Vanberkel, Peter & Zhong, Xiang, 2022. "Predicting ambulance offload delay using a hybrid decision tree model," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    11. Li, Mengyu & Carter, Alix & Goldstein, Judah & Hawco, Terence & Jensen, Jan & Vanberkel, Peter, 2021. "Determining ambulance destinations when facing offload delays using a Markov decision process," Omega, Elsevier, vol. 101(C).
    12. Mengyu Li & Peter Vanberkel & Alix J. E. Carter, 2019. "A review on ambulance offload delay literature," Health Care Management Science, Springer, vol. 22(4), pages 658-675, December.

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