L\'evy-driven Fluid Queue with Server Breakdowns and Vacations

TL;DR

This paper models a complex Le9vy-driven fluid queue with server breakdowns, vacations, and repairs, deriving the distribution of waiting times and analyzing system properties using advanced stochastic methods.

Contribution

It introduces a novel approach to analyze Le9vy-driven queues with server failures and vacations, providing explicit distribution results and system property insights.

Findings

Derived the limiting distribution of virtual waiting time.

Analyzed the busy period and correlation structure.

Established stochastic decomposition properties.

Abstract

In this paper, we consider a L\'evy-driven fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when he finds an empty system. We cast the queueing process as a L\'evy process modified to have random jumps at two classes of stopping times. By using the Kella-Whitt martingale method, we obtain the limiting distribution of the virtual waiting time process. Moreover, we investigate the busy period, the correlation structure and the stochastic decomposition properties. These results may be generalized to L\'evy processes with multi-class jump inputs or L\'evy-driven queues with multiple input classes.