Abstract
In this paper, I analyze the distributional properties of the busy period in an on-off fluid queue and the first passage time in a fluid queue driven by a finite state Markov process. In particular, I show that the first passage time has a IFR distribution and the busy period in the Anick-Mitra-Sondhi model has a DFR distribution.
Highlights
Fluid queues are used to represent systems where some quantity accumulates or is gradually depleted over time, subject to some random environment
= ri ; The main goal of this article is to analyze the distributional properties of the busy periods and the first passage times in the fluid queue theory
We prove that in the first fluid model, the busy periods starting with an activity period of fixed source—say, ith—have a completely monotone density function, they have a decreasing failure rate
Summary
Fluid queues are used to represent systems where some quantity accumulates or is gradually depleted over time, subject to some random (usually Markov) environment. N) are exponentially distributed with parameter λi , whereas the activity periods are generally distributed with distribution function Ai . = ri ; The main goal of this article is to analyze the distributional properties of the busy periods and the first passage times in the fluid queue theory.
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