Single Server Queueing Models

  • Wallace J. Hopp
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 115)

Queues or waiting lines form in systems when service times and arrival rates are variable. Simple queueing models provide insight into how variability subtly causes congestion. Understanding this is vital to the design and management of a wide range of production and service systems.


Service Time Arrival Rate Call Center Busy Period Interarrival Time 
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  1. Buzacott, J. and J.G. Shantikumar. (1993) Stochastic Models of Manufacturing Systems. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  2. Erlang, A.K. (1909) “The theory of probabilities and telephone conversations,” Nyt Tidsskrift for Matematik B 20, 33–39.Google Scholar
  3. Erlang, A.K. (1917) “Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges,” Elektrotkeknikeren 13, 5–13.Google Scholar
  4. Green, L.V. and P.J. Kolesar. (2004) “Applying management science to emergency response systems: Lessons from the past,” Management Science 50(8), 1001–1014.CrossRefGoogle Scholar
  5. Hopp, W. and M. Spearman. (2000) Factory Physics: Foundations of Manufacturing Management. McGraw-Hill, New York.Google Scholar
  6. Jackson, J.R. (1957) “Networks of waiting lines,” Operations Research 5, 518–521.CrossRefGoogle Scholar
  7. Jackson, J.R. (1963) “Jobshop-like queueing systems,” Management Science 10, 131–142.CrossRefGoogle Scholar
  8. Kendall, D.G. (1951) “Some problems in the theory of queues,” Journal of the Royal Statistical Society B 13, 151–185.Google Scholar
  9. Kendall, D.G. (1953) “Stochastic processes occurring in the theory of queues and their analysis by the method of the embedded Markov chain,” Annals of Mathematical Statistics 24, 338–354.CrossRefGoogle Scholar
  10. Khintchine, A. (1932) “Mathematical theory of a stationary queue,” Mathematicheskii Schornik 39, 73–84.Google Scholar
  11. Kingman, J.F.C. (1966) “On the algebra of queues,” Journal of Applied Probability 3, 285–326.CrossRefGoogle Scholar
  12. Kleinrock, L. (2002) “Creating a mathematical theory of computer networks,” Operations Research 50, 125–131.CrossRefGoogle Scholar
  13. Larson, R. (1972) Urban Police Patrol Analysis. MIT Press, Cambridge, MA.Google Scholar
  14. Larson, R. and A. Odoni. (1981) Urban Operations Research. Prentice-Hall, New York.Google Scholar
  15. Lindley, D.V. (1952). The theory of queues with a single server. Proceedings of the Cambridge Philosopical Society 48, 277–289.CrossRefGoogle Scholar
  16. Newell, G.F. (1982). Applications of Queueing Theory. 2nd edn., Chapman & Hall, New York.Google Scholar
  17. Pollaczek, F. (1934). Uber das waterproblem. Mathematische Zeitschrift 32, 492–537.CrossRefGoogle Scholar
  18. Stidham, S. (2002). Analysis, design, and control of queueing systems. Operations Research 50(1), 197–216.CrossRefGoogle Scholar
  19. Wein, L.M., D.L. Craft and E.H. Kaplan. (2003). Emergency response to an anthrax attack. Proceedings of the National Academy of Science 100(7), 4346–4351.CrossRefGoogle Scholar
  20. Whitt, W. (1983). The queueing network analyzer. Bell System Technical Journal 62, 2779–2815.Google Scholar

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© Springer Science + Business Media, LLC 2008

Authors and Affiliations

  • Wallace J. Hopp

There are no affiliations available

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