Distributional Properties of Fluid Queues Busy Period and First Passage Times

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.

Keywords

• fluid queue
• busy period
• IFR and DFR distributions
• Laplace transform