Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Hypercube queueing model

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_429

The hypercube queueing model was developed in the late 1960s and early 1970s, a period driven by a national commitment to devote scientific energies to our country's urban ills. The initial application focus for the model was the deployment of urban police patrol cars. Issues that could be examined with the model involved determining appropriate numbers of cars to allocate in each part of the city, spatially deploying the cars to police “beats” or other territories and evaluating the impact of alternative dispatch policies. Over the years, the model has been applied to a large number of police departments and to other services as well, both public and private.

In this article, we review the history of the model's development, the key ideas of the model and its implementation. Since the technology is more than 20 years old, there are numerous references in the literature providing technical details of various aspects of the model. Our purposes here are to describe the historical...

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  1. [1]
    Bodily, S.E. (1978). “Police Sector Design Incorporating Preferences of Interest Groups for Equality and Efficiency,” Management Science, 24, 1301–1313. Google Scholar
  2. [2]
    Brandeau, M. and Larson, R.C. (1986). “Extending and Applying the Hypercube Queueing Model to Deploy Ambulances in Boston,” in Delivery of Urban Services, A. Swersey and E. Ignall, eds., North Holland, New York.Google Scholar
  3. [3]
    Campbell, G.L. (1972). “A Spatially Distributed Queueing Model for Police Patrol Sector Design,” S.M. thesis, M.I.T., Cambridge, Massachusetts.Google Scholar
  4. [4]
    Chelst, K. (1975). “Implementing the Hypercube Model in the New Haven Department of Police Services,” The New York City Rand Institute, R-1566/7. Google Scholar
  5. [5]
    Chelst, K. (1978). “An Interactive Approach to Police Sector Design,” in R.C. Larson, ed., Police Deployment, New Tools for Planners, D.C. Heath, Lexington, Massachusetts.Google Scholar
  6. [6]
    Chelst, K. and Barlach, Z. (1981). “Multiple Unit Dispatches in Emergency Services: Models to Estimate System Performance,” Management Science, 27, 1390–1409.Google Scholar
  7. [7]
    Heller, N. (1977). “Field Evaluation of the Hypercube System for the Analysis of Police Patrol Operations: Final Report,” The Institute for Public Program Analysis, St. Louis, Missouri.Google Scholar
  8. [8]
    Hill. E.D. et al. (1981). “Planning for Emergency Ambulance Service Systems, City of Boston,” Department of Health and Hospitals, Massachusetts.Google Scholar
  9. [9]
    Jarvis, J.P. (1975). “Optimization in Stochastic Service Systems with Distinguishable Servers,” M.I.T. Ph.D. thesis, Cambridge, Massachusetts. Google Scholar
  10. [10]
    Larson, R.C. (1969). “Models for the Allocation of Urban Police Patrol Forces,” Tech. Rep. #44, Operations Research Center, M.I.T., Cambridge, Massachusetts.Google Scholar
  11. [11]
    Larson, R.C. (1971). “Measuring the Response Patterns of New York City Police Patrol Cars,” New York City Rand Institute R-673-NYC/HUD. Google Scholar
  12. [12]
    Larson, R.C. (1974a). “A Hypercube Queueing Modeling for Facility Location and Redistricting in Urban Emergency Services,” Jl. Computers and Operations Research, 1, 67–95.Google Scholar
  13. [13]
    Larson, R.C. (1974b). “Illustrative Police Sector Redesign in District 4 in Boston,” Urban Analysis 2(1), 51–91.Google Scholar
  14. [14]
    Larson, R.C. (1975a). “Approximating the Performance of Urban Emergency Service Systems,” Operations Research 23, 845–868.Google Scholar
  15. [15]
    Larson, R.C. (1975b). “Computer Program for Calculating the Performance of Urban Emergency Service Systems: User's Manual (Batch Processing),” Innovative Resource Planning in Urban Public Safety Systems, Report TR-14-75, M.I.T., Cambridge, Massachusetts.Google Scholar
  16. [16]
    Larson, R.C. (1979). “Structural System Models for Locational Decisions: An Example Using the Hyper-cube Queueing Model,” in Operational Research '78, Proceedings of the Eighth IFORS International Conference on Operations Research, K.B. Haley, ed., North-Holland, Amsterdam.Google Scholar
  17. [17]
    Larson, R.C., ed. (1978). Police Deployment: New Tools for Planners. Lexington Books, Massachusetts.Google Scholar
  18. [18]
    Larson, R.C. (1982). “Ambulance Deployment with the Hypercube Queueing Model,” Medical Instrumentation 16, 199–201.Google Scholar
  19. [19]
    Larson, R.C. and Franck, E. (1978). “Evaluating Dispatching Consequences of Automatic Vehicle Location in Emergency Services,” Jl. Computers and Operations Research, 5, 11–30.Google Scholar
  20. [20]
    Larson, R.C. and Li, V.O.K. (1981). “Finding Minimum Rectilinear Distance Paths in the Presence of Barriers,” Networks 11, 285–304.Google Scholar
  21. [21]
    Larson, R.C. and McEwen, T. (1974). “Patrol Planning in the Rotterdam Police Department,” Jl. Criminal Justice 2, 235–238.Google Scholar
  22. [22]
    Larson, R.C. and McKnew, M.A. (1982). “Police Patrol-Initiated Activities within a System Queueing Model,” Management Science 28, 759–774.Google Scholar
  23. [23]
    Larson, R.C. and Odoni, A.R. (1981). Urban Operations Research. Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
  24. [24]
    Larson, R.C. and Rich, T. (1987). “Travel Time Analysis of New York City Police Patrol Cars,” Interfaces 17(2), 15–20.Google Scholar
  25. [25]
    Li, V.O.K. (1977). “Testing the Hypercube Model in the New York City Police Department,” S.B. thesis, EE, M.I.T., Cambridge, Massachusetts.Google Scholar
  26. [26]
    McKnew, M. (1978). “The Performance of Initiated Activities and Their Impact on Resource Allocation,” M.I.T. Ph.D. thesis, Cambridge, Massachusetts. Google Scholar
  27. [27]
    Sacks, S.R. and Grief, S. (1994). “Orlando Magic,” OR/MS Today, 21(1), 30–32.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA