Standard Article

Large Deviations in Queueing Systems

  1. Ayalvadi J. Ganesh

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0449

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Ganesh, A. J. 2011. Large Deviations in Queueing Systems. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of Bristol, Department of Mathematics, Bristol, UK

Publication History

  1. Published Online: 15 FEB 2011

Abstract

Large deviations theory deals with fluctuations of random variables from their mean values on larger scales than the central limit scaling. When applied to queueing systems, it provides an elegant unified framework for estimating the probability distributions of queue sizes and waiting times or, more precisely, their tail decay rates. This article provides a brief introduction to large deviation theory as well as its application to some simple queueing models.

Keywords:

  • queueing model;
  • large-deviation principle;
  • contraction principle;
  • moderate deviation principle