An analysis of the ei/ek/l queueing system by restricted minimal lattice paths

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

Research output: Contribution to journalArticlepeer-review

2 Citations (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/Ejl and EjEjl 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


  • Combinatorial theory
  • Equilibrium probability distribution
  • Minimal lattice paths
  • Queue¬ing systems

ASJC Scopus subject areas

  • Management Information Systems
  • Strategy and Management
  • Management Science and Operations Research
  • Marketing


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