Occupation times for the finite buffer fluid queue with phase-type ON-times

TL;DR

This paper analyzes the occupation time distribution in a finite buffer fluid queue with phase-type ON-times, providing a method to compute the distribution function using an alternating sequence of sojourn times.

Contribution

It introduces a novel approach to determine the occupation time distribution in a finite buffer fluid queue with phase-type ON-times using an alternating sequence of i.i.d. sojourn times.

Findings

Derived the distribution function of occupation time in the queue.

Established a method using double transforms for analysis.

Applicable to queues with phase-type ON-times.

Abstract

In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed target level. We construct an alternating sequence of sojourn times $D_1,U_1,...$ where the pairs $(D_i,U_i)_{i\in\mathbb{N}}$ are i.i.d. random vectors. We use this sequence to determine the distribution function of the occupation time in terms of its double transform.