Queueing Systems

, Volume 43, Issue 1, pp 103–128

A Diffusion Approximation for a Markovian Queue with Reneging

  • Amy R. Ward
  • Peter W. Glynn

DOI: 10.1023/A:1021804515162

Cite this article as:
Ward, A.R. & Glynn, P.W. Queueing Systems (2003) 43: 103. doi:10.1023/A:1021804515162


Consider a single-server queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establish that this system can be approximated by either a reflected Ornstein–Uhlenbeck process or a reflected affine diffusion when the arrival rate exceeds or is close to the processing rate and the reneging rate is close to 0. We further compare the quality of the steady-state distribution approximations suggested by each diffusion.

Markovian queuesrenegingimpatiencedeadlinesreflected Ornstein–Uhlenbeck processreflected affine diffusiondiffusion approximationsteady-state

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Amy R. Ward
    • 1
  • Peter W. Glynn
    • 2
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Management Science & EngineeringStanford UniversityStanfordUSA