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An approximate hypercube model for public service systems with co-located servers and multiple response

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  • Ansari, Sardar
  • Yoon, Soovin
  • Albert, Laura A.

Abstract

Spatial queueing models help to evaluate the design of public safety systems such as fire, emergency medical service, and police departments, where vehicles are sent to geographically dispersed calls for service. We propose a new approximate hypercube spatial queueing model that allows for multiple servers to be located at the same station as well as multiple servers to be dispatched to a single call. We introduce the M[G]/M/s/s queueing model as an extension to the M/M/s/s model which allows for a single customer to request multiple servers with a general discrete probability distribution G. We use the M[G]/M/s/s queueing model to derive approximate formulas for the hypercube spatial queueing outputs. A simulation study validates the accuracy of the queueing approximations. Computational results suggest that the models are effective in evaluating the performance of emergency systems.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transe:v:103:y:2017:i:c:p:143-157
    DOI: 10.1016/j.tre.2017.04.013
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    1. Mark S. Daskin, 1983. "A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution," Transportation Science, INFORMS, vol. 17(1), pages 48-70, February.
    2. Richard C. Larson, 1975. "Approximating the Performance of Urban Emergency Service Systems," Operations Research, INFORMS, vol. 23(5), pages 845-868, October.
    3. Jonathan Halpern, 1977. "The Accuracy of Estimates for the Performance Criteria in Certain Emergency Service Queueing Systems," Transportation Science, INFORMS, vol. 11(3), pages 223-242, August.
    4. Marianov, Vladimir & ReVelle, Charles, 1996. "The Queueing Maximal availability location problem: A model for the siting of emergency vehicles," European Journal of Operational Research, Elsevier, vol. 93(1), pages 110-120, August.
    5. Resham Vinayak & S. Dharmaraja & Viswanathan Arunachalam, 2014. "On the study of simultaneous service by random number of servers with retrial and preemptive priority," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 20(1), pages 68-90.
    6. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    7. Fletcher, G. Y. & Perros, H. G. & Stewart, W. J., 1986. "A queueing system where customers require a random number of servers simultaneously," European Journal of Operational Research, Elsevier, vol. 23(3), pages 331-342, March.
    8. 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.
    9. Kathleen Hogan & Charles ReVelle, 1986. "Concepts and Applications of Backup Coverage," Management Science, INFORMS, vol. 32(11), pages 1434-1444, November.
    10. 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.
    11. 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.
    12. 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.
    13. Mark S. Daskin & Edmund H. Stern, 1981. "A Hierarchical Objective Set Covering Model for Emergency Medical Service Vehicle Deployment," Transportation Science, INFORMS, vol. 15(2), pages 137-152, May.
    14. Iannoni, Ana Paula & Morabito, Reinaldo, 2007. "A multiple dispatch and partial backup hypercube queuing model to analyze emergency medical systems on highways," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(6), pages 755-771, November.
    15. Richard C. Larson & Mark A. Mcknew, 1982. "Police Patrol-Initiated Activities Within a Systems Queueing Model," Management Science, INFORMS, vol. 28(7), pages 759-774, July.
    16. Andrew F. Seila, 1984. "Technical Note—On Waiting Times for a Queue in Which Customers Require Simultaneous Service from a Random Number of Servers," Operations Research, INFORMS, vol. 32(5), pages 1181-1184, October.
    17. Laura McLay, 2009. "A maximum expected covering location model with two types of servers," IISE Transactions, Taylor & Francis Journals, vol. 41(8), pages 730-741.
    18. J. P. Jarvis, 1985. "Approximating the Equilibrium Behavior of Multi-Server Loss Systems," Management Science, INFORMS, vol. 31(2), pages 235-239, February.
    19. Linda Green, 1981. "Comparing Operating Characteristics of Queues in Which Customers Require a Random Number of Servers," Management Science, INFORMS, vol. 27(1), pages 65-74, January.
    20. Charles ReVelle & Kathleen Hogan, 1989. "The Maximum Availability Location Problem," Transportation Science, INFORMS, vol. 23(3), pages 192-200, August.
    21. Richard C. Larson & Thomas F. Rich, 1987. "Travel-Time Analysis of New York City Police Patrol Cars," Interfaces, INFORMS, vol. 17(2), pages 15-20, April.
    22. Linda Green, 1984. "A Multiple Dispatch Queueing Model of Police Patrol Operations," Management Science, INFORMS, vol. 30(6), pages 653-664, June.
    23. F C Mendonça & R Morabito, 2001. "Analysing emergency medical service ambulance deployment on a Brazilian highway using the hypercube model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 261-270, March.
    24. Linda Green & Peter Kolesar, 1984. "A Comparison of the Multiple Dispatch and M/M/c Priority Queueing Models of Police Patrol," Management Science, INFORMS, vol. 30(6), pages 665-670, June.
    25. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.
    26. Geroliminis, Nikolas & Karlaftis, Matthew G. & Skabardonis, Alexander, 2009. "A spatial queuing model for the emergency vehicle districting and location problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 798-811, August.
    27. Percy H. Brill & Linda Green, 1984. "Queues in Which Customers Receive Simultaneous Service from a Random Number of Servers: A System Point Approach," Management Science, INFORMS, vol. 30(1), pages 51-68, January.
    28. 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.
    29. Kenneth Chelst & James P. Jarvis, 1979. "Technical Note—Estimating the Probability Distribution of Travel Times for Urban Emergency Service Systems," Operations Research, INFORMS, vol. 27(1), pages 199-204, February.
    30. Linda Green, 1980. "A Queueing System in Which Customers Require a Random Number of Servers," Operations Research, INFORMS, vol. 28(6), pages 1335-1346, December.
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