Analysis of the El/Ek/1 queueing system by restricted minimal lattice paths

Ikuo Arizono, Hiroshi Ohta, Stuart J. Deutsch, Ching Cheng Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The usual procedure for obtaining the equilibrium probability distribution of the queue length in a queueing system is by constructing and solving the difference-differential equations. In this paper, a new approach for deriving the equilibrium probability distributions of the queue length in the M/M/1, M/Ek/1 and El/Ek/1 queueing systems is presented, based on the generating function of the number of the minimal lattice paths. The proposed procedure obtains the equilibrium probability distribution more easily than the usual procedure, which solves difference-differential equations.

Original languageEnglish
Pages (from-to)245-253
Number of pages9
JournalJournal of the Operational Research Society
Volume46
Issue number2
Publication statusPublished - Feb 1995
Externally publishedYes

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Probability distributions
Differential equations
Probability distribution
Queueing system
Queue
Generating function

ASJC Scopus subject areas

  • Management of Technology and Innovation
  • Strategy and Management
  • Management Science and Operations Research

Cite this

Analysis of the El/Ek/1 queueing system by restricted minimal lattice paths. / Arizono, Ikuo; Ohta, Hiroshi; Deutsch, Stuart J.; Wang, Ching Cheng.

In: Journal of the Operational Research Society, Vol. 46, No. 2, 02.1995, p. 245-253.

Research output: Contribution to journalArticle

Arizono, Ikuo ; Ohta, Hiroshi ; Deutsch, Stuart J. ; Wang, Ching Cheng. / Analysis of the El/Ek/1 queueing system by restricted minimal lattice paths. In: Journal of the Operational Research Society. 1995 ; Vol. 46, No. 2. pp. 245-253.
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