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The G/M/1 Queue

  1. David Perry

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0880

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Perry, D. 2011. The G/M/1 Queue. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of Haifa, Department of Statistics, Haifa, Israel

Publication History

  1. Published Online: 15 FEB 2011

Abstract

The M/G/1 queue and the G/M/1 queue represent the mainstay of the single server queueing models. Both models are obtained as special cases of the G/G/1 queue for which most of the relevant measures and functionals cannot be expressed in closed form formulas. This review is a direct continuation of the encyclopedia entry “The M/G/1 queue”, and the spirit follows the same direction of that article in the sense that we focus on the same measure and functionals. The approach here is based on the special duality between the M/G/1 queue and the G/M/1 queue so that one can use known results of the M/G/1 queue to derive properties into the G/M/1 queue.

Keywords:

  • single server queue;
  • M/G/1 queue;
  • G/M/1 queue;
  • steady state;
  • number of customers;
  • attained waiting time;
  • sojourn time;
  • busy period;
  • idle period