Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

BIRTH-DEATH PROCESS

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_77

A stochastic counting process that satisfies the following is called a birth-death process: (1) changes from state n (sometimes written more generally as state En) may only be to states n + 1 or n − 1 (i.e., changes can only be ± 1 unit); (2) the probability of a birth (death) occurring in the “small” interval of time, (t, t + dt), given that the process was in state n at the start of the interval, is λndt + o(dt)[μndt + o(dt)], where o(dt) is a function going to 0 faster than dt. Such processes are in fact Markov chains in continuous time. The system size of an M/M/1 queueing system is an example of a birth-death process where λn = λ(n = 0, 1, 2, ...) and μn = μ (n = 1, 2, ...).  Markov chains;  Markov processes.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA