Exact analysis of transient behavior of finite-capacity MAP-driven queues

Michel Mandjes; Daniël Rutgers; Werner Scheinhardt

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arXiv · 2602.09676

Exact analysis of transient behavior of finite-capacity MAP-driven queues

Michel Mandjes·Daniël Rutgers·Werner Scheinhardt

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Abstract

This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed time, thereby uniquely characterizing its transient distribution. The proposed approach combines several decompositions with established fluctuation-theoretic results for spectrally one-sided L\'evy processes. For the special case of Markov-modulated compound Poisson input, we additionally derive results for the idle time and the cumulative amount of lost work. We conclude this paper with a series of numerical experiments.

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BibTeX RIS

Michel Mandjes, Daniël Rutgers, Werner Scheinhardt. 2026-02-10. Exact analysis of transient behavior of finite-capacity MAP-driven queues. https://arxiv.org/abs/2602.09676

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