Encyclopedia of Operations Research and Management Science

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

Memoryless property

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_610

For stochastic processes, lack-of-memory is synonymous with the Markov property. For a positive random variable T that models the duration of some phenomenon, lack-of-memory means that the time remaining is independent of the time already passed, that is, Pr{T > t + s|T > s} = Pr{T > t} for s, t > 0. The exponential distribution is the only continuous distribution with lack-of-memory, while the geometric distribution is the only discrete distribution with lack-of-memory.  Exponential arrivals; Markov processes; Markov property.

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