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On the time-dependent behavior of preemptive single-server queueing systems with Poisson arrivals

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Abstract

We present a detailed study of the time-dependent behavior of both the queue-length process and the workload process of various types of preemptive Last-Come-First-Served queueing systems, such as the preemptive repeat different and preemptive repeat identical models recently studied in Asmussen and Glynn (Queue Syst 87:1–22, 2017) and Bergquist and Sigman (Stoch Models 38:515–544, 2022). Our main results show that various quantities that provide information about the time-dependent behavior of these processes can be expressed in terms of the Laplace-Stieltjes transform of the busy period, and we show how a natural coupling procedure can be used to establish, for each preemptive queue we consider, a recursive procedure for calculating these busy period transforms on the set of all complex numbers having positive real part.

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Acknowledgements

The author wishes to thank two anonymous referees for providing many useful comments on an earlier draft of this manuscript.

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  1. School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, USA

    Brian Fralix

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  1. Brian Fralix
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Correspondence to Brian Fralix.

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Fralix, B. On the time-dependent behavior of preemptive single-server queueing systems with Poisson arrivals. Queueing Syst 107, 31–61 (2024). https://doi.org/10.1007/s11134-024-09905-2

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