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

TL;DR

This paper derives the Laplace-Stieltjes transform of workload distribution at exponential times for finite-capacity queues driven by spectrally one-sided MAPs, providing insights into their transient behavior.

Contribution

It offers a novel analytical framework combining decompositions and fluctuation theory to characterize transient workload distributions in MAP-driven queues.

Findings

Laplace-Stieltjes transform of workload at exponential times derived

Results for idle time and lost work in Markov-modulated compound Poisson case

Numerical experiments illustrating theoretical findings

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.