Transient and busy period analysis of the GI/G/1 queue: The method of stages

Dimitris J. Bertsimas, Daisuke Nakazato

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

In this paper we study the transient behavior of the MGEL/MGEM/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.

Original languageEnglish
Pages (from-to)153-184
Number of pages32
JournalQueueing Systems
Volume10
Issue number3
DOIs
Publication statusPublished - 1992 Sep
Externally publishedYes

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Laplace transforms
Algebra
Tensors
Queue

Keywords

  • busy period
  • linear algebra
  • transform methods
  • Transient analysis

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

Transient and busy period analysis of the GI/G/1 queue : The method of stages. / Bertsimas, Dimitris J.; Nakazato, Daisuke.

In: Queueing Systems, Vol. 10, No. 3, 09.1992, p. 153-184.

Research output: Contribution to journalArticle

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