Acta Informatica

, Volume 28, Issue 8, pp 801–815 | Cite as

Approximating queue lengths inM(t)/G/1 queue using the maximum entropy principle

  • Attahiru Sule Alfa
  • Mingyuan Chen


Using the discrete time approach a model is developed for obtaining the expected queue length of theM(t)/G/1 queue. This type of queue occurs in different forms in transportation and traffic systems and in communications and manufacturing systems. In order to cut down the very high computational efforts required to evaluate the performance measures in such queues by exact methods, the Maximum Entropy Principle is used to approximate the expected queue length which is one of the most commonly used performance measures. A procedure is then developed for reducing the error encountered when this approximation is adopted. The results from this paper will encourage the practitioners to use the appropriate time-varying queueing models when the need arises instead of resorting to very poor approximations.


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  1. 1.
    Alfa, A.S.: Approximating queue lengths inM(t)/D/1 queue. Eur. J. Oper. Res.44, 60–66 (1990)Google Scholar
  2. 2.
    Dafermos, S.C., Neuts, M.F.: A single server queue in discrete time. Cah. Cent. Etud. Rech. Oper.13, 23–40 (1971)Google Scholar
  3. 3.
    El-Affendi, M.A., Kouvatsos, D.: A maximum entropy analysis of theM/G/1 andG/M/1 queueing systems at equilibrium. Acta Inf.19, 339–335 (1983)Google Scholar
  4. 4.
    Guiasu, S.: Maximum entropy condition in queueing theory. J Oper. Res. Soc.37, 293–301 (1986)Google Scholar
  5. 5.
    Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev.104, 620–630 (1957)Google Scholar
  6. 6.
    Kouvatsos, D.D.: A maximum entropy analysis of theG/G/1 queue at equilibrium. J. Oper. Res. Soc.39, 183–200 (1988)Google Scholar
  7. 7.
    Minh, D.L.: The discrete-time single server' queue with time-imhomogenous compound Poisson input. J Appl. Probab.15, 590–601 (1978)Google Scholar
  8. 8.
    Moore, S.C.: Approximating the behaviour of nonstationary single-server queue. Oper. Res.23, 1011–1032 (1975)Google Scholar
  9. 9.
    Rego, V., Szpankowski, W.: The presence of exponentiality in entropy maximizedM/GI/1 queues. Comput. Oper. Res.16, 441–449 (1989)Google Scholar
  10. 10.
    Rothkopf, M.H., Oren, S.S.: A closure approximation for the nonstationaryM/M/s queue. Manag. Sci.25, 522–534 (1979)Google Scholar
  11. 11.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J.27, 379–423, 623–656 (1948)Google Scholar
  12. 12.
    Shore, J.E.: Information theoretic approximations forM/G/1 andG/G/1 queuing systems. Acta Inf.17, 43–61 (1982)Google Scholar
  13. 13.
    Taaffe, M.R., Ong, K.L.: Approximating nonstationaryPh(t)/Ph(t)/1/c queueing systems. Research Memorandum, 85-5, School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907 (1985)Google Scholar
  14. 14.
    Wu, J.-S., Chan, W.C.: Maximum entropy analysis of multiple-server queueing systems. J. Oper. Res. Soc.40, 815–825 (1989)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Attahiru Sule Alfa
    • 1
  • Mingyuan Chen
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of ManitobaWinnipegCanada

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