Health Care Management Science

, Volume 21, Issue 4, pp 517–533 | Cite as

An expected coverage model with a cutoff priority queue

  • Soovin Yoon
  • Laura A. AlbertEmail author


Emergency medical services provide immediate care to patients with various types of needs. When the system is congested, the response to urgent emergency calls can be delayed. To address this issue, we propose a spatial Hypercube approximation model with a cutoff priority queue that estimates performance measures for a system where some servers are reserved exclusively for high priority calls when the system is congested. In the cutoff priority queue, low priority calls are not immediately served—they are either lost or entered into a queue—whenever the number of busy ambulances is equal to or greater than the cutoff. The spatial Hypercube approximation model can be used to evaluate the design of public safety systems that employ a cutoff priority queue. A mixed integer linear programming model uses the Hypercube model to identify deployment and dispatch decisions in a cutoff priority queue paradigm. Our computational study suggests that the improvement in the expected coverage is significant when the cutoff is imposed, and it elucidates the tradeoff between the coverage improvement and the cost to low-priority calls that are “lost” when using a cutoff. Finally, we present a method for selecting the cutoff value for a system based on the relative importance of low-priority calls to high-priority calls.


Coverage model Cutoff priority queue Emergency medical services ambulance location Hypercube approximation Simulation 



This work was funded by the National Science Foundation [Awards 1444219, 1361448]. The views and conclusions contained in this document are those of the author and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the National Science Foundation. The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.


  1. 1.
    Ansari S, McLay LA, Mayorga ME (2015) A maximum expected covering problem for district design. Transp Sci 51(1):376– 390CrossRefGoogle Scholar
  2. 2.
    Aringhieri R, Bruni M, Khodaparasti S, van Essen J (2017) Emergency medical services and beyond: addressing new challenges through a wide literature review. Comput Oper Res 78:349– 368CrossRefGoogle Scholar
  3. 3.
    Aringhieri R, Carello G, Morale D (2016) Supporting decision making to improve the performance of an italian emergency medical service. Ann Oper Res 236(1):131–148CrossRefGoogle Scholar
  4. 4.
    Batta R, Dolan JM, Krishnamurthy NN (1989) The maximal expected covering location problem: Revisited. Transp Sci 23(4):277–287CrossRefGoogle Scholar
  5. 5.
    Benn BA (1966) Hierarchical car pool systems in railroad transportation. Ph.D. thesis, Case Institute of Technology, ClevelandGoogle Scholar
  6. 6.
    Boyaci B, Geroliminis N (2015) Approximation methods for large-scale spatial queueing systems. Transportational Res B Methodol 74:151–181CrossRefGoogle Scholar
  7. 7.
    Brotcorne L, Laporte G, Semet F (2003) Ambulance location and relocation models. Eur J Oper Res 147(3):451–463CrossRefGoogle Scholar
  8. 8.
    Budge S, Ingolfsson A, Erkut E (2009) Technical note–approximating vehicle dispatch probabilities for emergency service systems with location-specific service times and multiple units per location. Oper Res 57 (1):251–255CrossRefGoogle Scholar
  9. 9.
    Burwell TH, Jarvis JP, McKnew MA (1993) Modeling co-located servers and dispatchties in the hypercube model. Comput Oper Res 20(2):113–119CrossRefGoogle Scholar
  10. 10.
    Cho SH, Jang H, Lee T, Turner J (2014) Simultaneous location of trauma centers and helicopters for emergency medical service planning. Oper Res 62(4):751–771CrossRefGoogle Scholar
  11. 11.
    Church R, ReVelle C (1974) The maximal covering location problem. Pap Reg Sci 32(1):101–118CrossRefGoogle Scholar
  12. 12.
    Daskin MS (1983) A maximum expected covering location model: formulation, properties and heuristic solution. Transp Sci 17(1):48–70CrossRefGoogle Scholar
  13. 13.
    Figueira G, Almada-Lobo B (2014) Hybrid simulation–optimization methods: a taxonomy and discussion. Simul Model Pract Theory 46:118–134CrossRefGoogle Scholar
  14. 14.
    Gendreau M, Laporte G, Semet F (2001) A dynamic model and parallel tabu search heuristic for real-time ambulance relocation. Parallel Comput 27(12):1641–1653CrossRefGoogle Scholar
  15. 15.
    Geroliminis N, Karlaftis MG, Skabardonis A (2009) A spatial queuing model for the emergency vehicle districting and location problem. Transp Res B Methodol 43(7):798–811CrossRefGoogle Scholar
  16. 16.
    Goldberg JB (2004) Operations research models for the deployment of emergency services vehicles. EMS Manag J 1(1):20–39Google Scholar
  17. 17.
    Iannoni AP, Morabito R (2007) A multiple dispatch and partial backup hypercube queuing model to analyze emergency medical systems on highways. Transp Res E Logist Trans Rev 43(6):755–771CrossRefGoogle Scholar
  18. 18.
    Ingolfsson A, Budge S, Erkut E (2008) Optimal ambulance location with random delays and travel times. Health Care Manag Sci 11:262–274CrossRefGoogle Scholar
  19. 19.
    Jagtenberg CJ, Bhulai S, der Mei RDV (2016) Dynamic ambulance dispatching: is the closest-idle policy always optimal? Health care management science (to appear)CrossRefGoogle Scholar
  20. 20.
    Jaiswal NK (1968) Priority queues. Academic Press, New YorkGoogle Scholar
  21. 21.
    Jarvis JP (1985) Approximating the equilibrium behavior of multi-server loss systems. Manag Sci 31(2):235–239CrossRefGoogle Scholar
  22. 22.
    Kim SH, Whitt W (2014) Are call center and hospital arrivals well modeled by non-homogeneous Poisson processes? Manuf Serv Oper Manag 16(3):464–480CrossRefGoogle Scholar
  23. 23.
    Kolesar P, Walker WE (1974) An algorithm for the dynamic relocation of fire companies. Oper Res 22 (2):249–274CrossRefGoogle Scholar
  24. 24.
    Larsen MP, Eisenberg MS, Cummins RO, Hallstrom AP (1993) Predicting survival from out-of-hospital cardiac arrest: a graphic model. Ann Emerg Med 22(11):1652–1658CrossRefGoogle Scholar
  25. 25.
    Larson RC (1974) A hypercube queuing model for facility location and redistricting in urban emergency services. Oper Res 1(1):67–95Google Scholar
  26. 26.
    Larson RC (1975) Approximating the performance of urban emergency service systems. Oper Res 23(5):845–868CrossRefGoogle Scholar
  27. 27.
    Maxwell MS, Restrepo M, Henderson SG, Topaloglu H (2010) Approximate dynamic programming for ambulance redeployment. INFORMS J Comput 22(2):266–281CrossRefGoogle Scholar
  28. 28.
    McLay LA (2009) A maximum expected covering location model with two types of servers. IIE Trans 41 (8):730–741CrossRefGoogle Scholar
  29. 29.
    McLay LA, Mayorga ME (2013) A Dispatching Model for Server-to-Customer Systems That Balances Efficiency and Equity. Manuf Serv Oper Manag 15(2):205–220CrossRefGoogle Scholar
  30. 30.
    McLay LA, Moore H (2012) Hanover county improves its response to emergency medical 911 patients. Interfaces 42(4):380–394CrossRefGoogle Scholar
  31. 31.
    Mendonċa F, Morabito R (2001) Analysing emergency medical service ambulance deployment on a Brazilian highway using the hypercube model. J Oper Res Soc, pp 261–270CrossRefGoogle Scholar
  32. 32.
    Rajagopalan H, Saydam C, Xiao J (2008) A multiperiod set covering location model for dynamic redeployment of ambulances. Comput Oper Res 35(3):814–826CrossRefGoogle Scholar
  33. 33.
    Restrepo M, Henderson S, Topaloglu H (2009) Erlang loss models for the static deployment of ambulances. Health Care Manag Sci 12:67–79CrossRefGoogle Scholar
  34. 34.
    Reuter-Oppermann M, van den Berg P, Vile J (2017) Logistics for emergency medical service systems. Health Syst. doi: 10.1057/s41306-017-0023-x CrossRefGoogle Scholar
  35. 35.
    Schaack C, Larson RC (1986) An n-server cutoff priority queue. Oper Res 34(2):257–266CrossRefGoogle Scholar
  36. 36.
    de Souza RM, Morabito R, Chiyoshi FY, Iannoni AP (2015) Incorporating priorities for waiting customers in the hypercube queuing model with application to an emergency medical service system in Brazil. Eur J Oper Res 242(1):274–285Google Scholar
  37. 37.
    Taylor IDS, Templeton JGC (1980) Waiting time in a multi-server cutoff-priority queue, and its application to an urban ambulance service. Oper Res 28(5):1168–1188CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Industrial & Systems Engineering DepartmentUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations