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

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  • Brian Fralix

    (Clemson University)

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.

Suggested Citation

  • Brian Fralix, 2024. "On the time-dependent behavior of preemptive single-server queueing systems with Poisson arrivals," Queueing Systems: Theory and Applications, Springer, vol. 107(1), pages 31-61, June.
    • Handle: RePEc:spr:queues:v:107:y:2024:i:1:d:10.1007_s11134-024-09905-2
    DOI: 10.1007/s11134-024-09905-2
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