Distributional properties of fluid queues busy period and first passage times

TL;DR

This paper investigates the distributional characteristics of busy periods and first passage times in fluid queues driven by Markov processes, revealing specific aging properties of these distributions in certain models.

Contribution

It demonstrates that in the Anick-Mitra-Sondhi model, the first passage time is IFR and the busy period is DFR, providing new insights into their aging properties.

Findings

First passage time has an increasing failure rate (IFR) distribution.

Busy period has a decreasing failure rate (DFR) distribution.

Results apply to fluid queues driven by finite state Markov processes.

Abstract

In this paper we analyze the distributional properties of a busy period in an on-off fluid queue and the a first passage time in a fluid queue driven by a finite state Markov process. In particular, we show that in Anick-Mitra-Sondhi model the first passage time has a IFR distribution and the busy period has a DFR distribution.