Exact overflow asymptotics for queues with many Gaussian inputs
- 1 September 2003
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 40 (3), 704-720
- https://doi.org/10.1239/jap/1059060897
Abstract
In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.Keywords
This publication has 21 references indexed in Scilit:
- Ruin probability for Gaussian integrated processesStochastic Processes and their Applications, 2001
- Large Deviations for Small Buffers: An Insensitivity ResultQueueing Systems, 2001
- Extremes of a certain class of Gaussian processesStochastic Processes and their Applications, 1999
- Large buffer asymptotics for the queue with fractional Brownian inputJournal of Applied Probability, 1999
- Cell loss asymptotics for buffers fed with a large number of independent stationary sourcesJournal of Applied Probability, 1999
- On–off fluid models in heavy traffic environmentQueueing Systems, 1999
- A Gaussian fluid modelQueueing Systems, 1995
- Fluid Model Driven by an Ornstein-Uhlenbeck ProcessProbability in the Engineering and Informational Sciences, 1994
- On the self-similar nature of Ethernet traffic (extended version)IEEE/ACM Transactions on Networking, 1994
- Extreme values of the cyclostationary Gaussian random processJournal of Applied Probability, 1993