The physics of the Mt/G/ ∞ symbol Queue
Operations Research
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
The last departure time from an Mt/G/∞ queue with a terminating arrival process
Queueing Systems: Theory and Applications
Two-Moment Approximations for Maxima
Operations Research
The last departure time from an Mt/G/∞ queue with a terminating arrival process
Queueing Systems: Theory and Applications
Two-parameter heavy-traffic limits for infinite-server queues
Queueing Systems: Theory and Applications
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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/驴 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.