Queueing Systems

, Volume 58, Issue 2, pp 77–104 | Cite as

The last departure time from an M t /G/∞ queue with a terminating arrival process

  • David Alan Goldberg
  • Ward WhittEmail author
Open Access


This paper studies the last departure time from a queue with a terminating arrival process. This problem is motivated by a model of two-stage inspection in which finitely many items come to a first stage for screening. Items failing first-stage inspection go to a second stage to be examined further. Assuming that arrivals at the second stage can be regarded as an independent thinning of the departures from the first stage, the arrival process at the second stage is approximately a terminating Poisson process. If the failure probabilities are not constant, then this Poisson process will be nonhomogeneous. The last departure time from an M t /G/∞ queue with a terminating arrival process serves as a remarkably tractable approximation, which is appropriate when there are ample inspection resources at the second stage. For this model, the last departure time is a Poisson random maximum, so that it is possible to give exact expressions and develop useful approximations based on extreme-value theory.


Queues with terminating arrival processes Last departure time Infinite-server queues Non-stationary queues Congestion caused by inspection Two-stage inspection Extreme-value theory 

Mathematics Subject Classification (2000)

60K25 60G70 90B22 


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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Operations Research CenterMITCambridgeUSA
  2. 2.IEOR DepartmentColumbia UniversityNew YorkUSA

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