Path Space Large Deviations of a Large Buffer with Gaussian Input Traffic
We consider a queue fed by Gaussian traffic and give conditions on the input process under which the path space large deviations of the queue are governed by the rate function of the fractional Brownian motion. As an example we consider input traffic that is composed of of independent streams, each of which is a fractional Brownian motion, having different Hurst indices.
Unable to display preview. Download preview PDF.
- R. Adler, An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, IMS Lecture Notes (1990).Google Scholar
- P. Billingsley, Convergence of Probability Measures, 2nd ed. (Wiley, New York, 1999).Google Scholar
- V.V. Buldygin and Yu.V. Kozachenko, Metric Characterization of Random Variables and Random Processes (Amer. Math. Soc., Providence, RI, 2000).Google Scholar
- V. Buldygin and V. Zaiats, A global asymptotic normality of the sample correlograms of a stationary Gaussian process, Random Operators Stochastic Equations 7(2) (1999) 109-132.Google Scholar
- A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 2nd ed. (Springer, New York, 1998).Google Scholar
- J.-D. Deuschel and D. Stroock, Large Deviations (Academic Press, New York, 1984).Google Scholar
- N.G. Duffield and N. O'Connel, Large deviations and overflow probabilities for the general singleserver queue, with applications. Proc. Cambridge Phil. Soc. 118(2) (1995) 363-374.Google Scholar
- Yu. Kozachenko and O. Vasilik, On the distribution of suprema of Sub?(?) random processes, Theory Stochastic Process. 4(20)(1/2) (1998) 147-160.Google Scholar
- I. Norros, A storage model with self-similar input, Queueing Systems 16 (1994) 387-396.Google Scholar
- I. Norros, Busy periods of fractional Brownian storage: A large deviations approach, Adv. in Performance Anal. 2(1) (1999) 1-19.Google Scholar