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

Brian Fralix ()
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Brian Fralix: Clemson University

Queueing Systems: Theory and Applications, 2024, vol. 107, issue 1, No 2, 61 pages

Abstract: 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.

Keywords: LIFO; Palm distribution; Preemptive resume; Preemptive repeat; Queue length; Workload; Primary 60K25; Secondary 60G55 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11134-024-09905-2

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