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The M/M/1 Queue

  1. Myron Hlynka

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0891

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

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

Author Information

  1. University of Windsor, Department of Mathematics and Statistics, Ontario, Canada

Publication History

  1. Published Online: 15 FEB 2011

Abstract

The M/M/1 queueing system is discussed. Key properties are stated, many with proofs. Steady state and transient probabilities are presented along with many other well-known properties. A variety of analytical techniques are used in the presentation. Graphs are used to illustrate several aspects of this system.

Keywords:

  • queueing;
  • Poisson process;
  • limiting probability;
  • transient probability;
  • PASTA;
  • level crossing;
  • laplace transform;
  • busy period;
  • birth and death process