Transient Behavior of Fractional Queues and Related Processes

Dexter O. Cahoy, Federico Polito, Vir Phoha

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian and Markovian properties which naturally provide greater flexibility in modeling real queue systems than its classical counterpart. Algorithms to simulate M/M/1 queue process and the related linear birth-death process are provided. Closed-form expressions of the point and interval estimators of the parameters of the proposed fractional stochastic models are also presented. These methods are necessary to make these models usable in practice. The proposed fractional M/M/1 queue model and the statistical methods are illustrated using financial data.

Original languageEnglish (US)
Pages (from-to)739-759
Number of pages21
JournalMethodology and Computing in Applied Probability
Issue number3
StatePublished - Sep 10 2015
Externally publishedYes


  • Fractional M/M/1 queue
  • Fractional birth-death process
  • Mittag–Leffler function
  • Parameter estimation
  • Simulation
  • Transient analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics


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