Abstract
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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Goldberg, D.A., Whitt, W. The last departure time from an M t /G/∞ queue with a terminating arrival process. Queueing Syst 58, 77–104 (2008). https://doi.org/10.1007/s11134-008-9060-2
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DOI: https://doi.org/10.1007/s11134-008-9060-2
Keywords
- Queues with terminating arrival processes
- Last departure time
- Infinite-server queues
- Non-stationary queues
- Congestion caused by inspection
- Two-stage inspection
- Extreme-value theory