Sample-path large deviations for generalized processor sharing queues with Gaussian inputs

Authors:
Michel Mandjes;Miranda van Uitert
Affiliations:
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands and Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Venue:
Performance Evaluation - Long range dependence and heavy tail distributions
Year:
2005

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Abstract

In this paper we consider the generalized processor sharing (GPS) mechanism serving two traffic classes. These classes consist of a large number of independent identically distributed Gaussian flows with stationary increments. We are interested in the logarithmic asymptotics or exponential decay rates of the overflow probabilities. We first derive both an upper and a lower bound on the overflow probability. Scaling both the buffer sizes of the queues and the service rate with the number of sources, we apply Schilder's sample-path large deviations theorem to calculate the logarithmic asymptotics of the upper and lower bound. We discuss in detail the conditions under which the upper and lower bound match. Finally we show that our results can be used to choose the values of the GPS weights. The results are illustrated by numerical examples.