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Birth-and-Death Processes

  1. Guvenc Degirmenci

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0111

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Degirmenci, G. 2011. Birth-and-Death Processes. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of Pittsburgh, Department of Industrial Engineering, Pittsburgh, Pennsylvania

Publication History

  1. Published Online: 14 JAN 2011

Abstract

A birth-and-death (BD) process is a continuous-time Markov chain on the nonnegative integers whose transitions are restricted to its nearest neighbors. These processes have enjoyed wide popularity in a diverse set of fields. This article formally defines the BD process, reviews basic results for its transient and asymptotic analysis, discusses some special cases, and describes two applications in queueing theory.

Keywords:

  • birth-and-death process;
  • Markov process;
  • population models;
  • queueing;
  • level dependent