Time-dependent behavior of fluid buffer models with Markov input and constant output rates
SIAM Journal on Applied Mathematics
Fluid models for single buffer systems
Frontiers in queueing
First Passage Times in Fluid Models with an Application to Two Priority Fluid Systems
IPDS '96 Proceedings of the 2nd International Computer Performance and Dependability Symposium (IPDS '96)
The busy period in the fluid queue
The busy period in the fluid queue
Busy period analysis for M/PH/1 queues with workload dependent balking
Queueing Systems: Theory and Applications
Introduction of first passage time (FPT) analysis for software reliability and network security
Proceedings of the 5th Annual Workshop on Cyber Security and Information Intelligence Research: Cyber Security and Information Intelligence Challenges and Strategies
A fluid model analysis of streaming media in the presence of time-varying bandwidth
Proceedings of the 24th International Teletraffic Congress
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A stochastic fluid queueing system describes the input-output flow of a fluid in a storage device, called a buffer. The rates at which the fluid enters and leaves the buffer depend on a random environment process. The external governing process is an irreducible CTMC and the fluid from the buffer is emptied at a constant rate @m. Let X(t) denote the buffer content at time t and I(t) denote the state of the random environment at time t. In this paper we present a method for computing the mean first passage times in the {X(t),t=0} process, as well as in the bivariate {(X(t),I(t)),t=0} process. We derive a system of first-order non-homogeneous linear differential equations for the mean first passage times which can easily be solved using well-known techniques. The method developed here can be readily implemented for computational purposes. We present two examples illustrating how to find explicitly the analytical solution to a small two-state problem and how to obtain numerical solutions to a multistate problem.