Busy period analysis, rare events and transient behavior in fluid flow models. (1994)

• Record Type: Journal Article
• Authors: Asmussen, Søren
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 3(1994)
• Page Start: 269
• Page End: 299
• Publication Date: 1994
• Subjects: Markov additive process -- skip-free -- buffer over-flow -- conditional limit theorems -- first passage time -- change of measure -- exponential family -- likelihood ratio identity -- extreme values -- quick simulation -- asynchronous transfer mode; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000262
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We consider a process { ( J t, V t ) } t ≥ 0 on E × [ 0, ∞ ), such that { J t } is a Markov process with finite state space E, and { V t } has a linear drift r i on intervals where J t = i and 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 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.