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

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

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1 Citation (Scopus)


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
Issue number2
Publication statusPublished - Feb 1995
Externally publishedYes


ASJC Scopus subject areas

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

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