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

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  • Søren Asmussen

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.

Suggested Citation

  • Søren Asmussen, 1994. "Busy period analysis, rare events and transient behavior in fluid flow models," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-31, January.
    • Handle: RePEc:hin:jnijsa:365297
    DOI: 10.1155/S1048953394000262
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    Cited by:

    1. V. Ramaswami, 2006. "Passage Times in Fluid Models with Application to Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 497-515, December.
    2. A. B. Dieker & M. Mandjes, 2011. "Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 221-267, June.

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