Busy period analysis, rare events and transient behavior in fluid flow models

Søren Asmussen
1994 Journal of Applied Mathematics and Stochastic Analysis  
We consider a process{(Jt,Vt)}t≥0onE×[0,∞), such that{Jt}is a Markov process with finite state spaceE, and{Vt}has a linear driftrion intervals whereJt=iand reflection at 0. Such a process arises as a fluid flow model of current interest in telecommunications engineering for the purpose of modeling ATM technology. We compute the mean of the busy period and related first passage times, show that the probability of buffer overflow within a busy cycle is approximately exponential, and give
more » ... , and give conditioned limit theorems for the busy cycle with implications for quick simulation. Further, various inequalities and approximations for transient behavior are given. Also explicit expressions for the Laplace transform of the busy period are found. Mathematically, the key tool is first passage probabilities and exponential change of measure for Markov additive processes.
doi:10.1155/s1048953394000262 fatcat:npge5ozeebefzh7jarpfk62owe