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Queueing Systems

, Volume 50, Issue 4, pp 371–400 | Cite as

A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging

  • Amy R. WardEmail author
  • Peter W. Glynn
Article

Abstract

Consider a single-server queue with a renewal arrival process and generally distributed processing times in which each customer independently reneges if service has not begun within a generally distributed amount of time. We establish that both the workload and queue-length processes in this system can be approximated by a regulated Ornstein-Uhlenbeck (ROU) process when the arrival rate is close to the processing rate and reneging times are large. We further show that a ROU process also approximates the queue-length process, under the same parameter assumptions, in a balking model. Our balking model assumes the queue-length is observable to arriving customers, and that each customer balks if his or her conditional expected waiting time is too large.

Keywords

deadlines reneging balking impatience GI/GI/1-GI queue Ornstein-Uhlenbeck process regulated diffusion reflected diffusion 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Management Science & EngineeringStanford UniversityStanfordUSA

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