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

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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.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA

    Amy R. Ward

  2. Department of Management Science & Engineering, Stanford University, Stanford, CA, 94305, USA

    Peter W. Glynn

Authors
  1. Amy R. Ward
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  2. Peter W. Glynn
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Correspondence to Amy R. Ward.

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Ward, A.R., Glynn, P.W. A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging. Queueing Syst 50, 371–400 (2005). https://doi.org/10.1007/s11134-005-3282-3

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  • DOI: https://doi.org/10.1007/s11134-005-3282-3

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