Transient analysis of one-sided L\'evy-driven queues

TL;DR

This paper studies the transient behavior of workload in Le9vy-driven queues at random times, providing explicit results for spectrally one-sided processes and approximations for workload metrics.

Contribution

It offers explicit transient analysis results for spectrally one-sided Le9vy input queues and develops approximations for workload metrics after deterministic times.

Findings

Explicit results for workload at random epochs in spectrally one-sided queues

Approximate formulas for mean workload after deterministic time

Laplace transform approximations for workload distribution

Abstract

In this paper we analyze the transient behavior of the workload process in a L\'evy input queue. We are interested in the value of the workload process at a random epoch; this epoch is distributed as the sum of independent exponential random variables. We consider both cases of spectrally one-sided L\'evy input processes, for which we succeed in deriving explicit results. As an application we approximate the mean and the Laplace transform of the workload process after a deterministic time.