Exact analysis of transient behavior of finite-capacity MAP-driven queues
Probability
2026-02-11 v1
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.
Keywords
Cite
@article{arxiv.2602.09676,
title = {Exact analysis of transient behavior of finite-capacity MAP-driven queues},
author = {Michel Mandjes and Daniël Rutgers and Werner Scheinhardt},
journal= {arXiv preprint arXiv:2602.09676},
year = {2026}
}