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Maximum Entropy Principle Based Estimation of Performance Distribution in Queueing Theory

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  • Dayi He
  • Ran Li
  • Qi Huang
  • Ping Lei

Abstract

In related research on queuing systems, in order to determine the system state, there is a widespread practice to assume that the system is stable and that distributions of the customer arrival ratio and service ratio are known information. In this study, the queuing system is looked at as a black box without any assumptions on the distribution of the arrival and service ratios and only keeping the assumption on the stability of the queuing system. By applying the principle of maximum entropy, the performance distribution of queuing systems is derived from some easily accessible indexes, such as the capacity of the system, the mean number of customers in the system, and the mean utilization of the servers. Some special cases are modeled and their performance distributions are derived. Using the chi-square goodness of fit test, the accuracy and generality for practical purposes of the principle of maximum entropy approach is demonstrated.

Suggested Citation

  • Dayi He & Ran Li & Qi Huang & Ping Lei, 2014. "Maximum Entropy Principle Based Estimation of Performance Distribution in Queueing Theory," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-9, September.
    • Handle: RePEc:plo:pone00:0106965
    DOI: 10.1371/journal.pone.0106965
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    References listed on IDEAS

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    1. Charalabos Skianis & Demetres Kouvatsos, 1998. "Arbitrary open queueing networks with server vacation periods and blocking," Annals of Operations Research, Springer, vol. 79(0), pages 143-180, January.
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