Paper Info
Title
Sample-path large deviations for generalized processor sharing queues with Gaussian inputs
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.
Year
DOI
Venue
2005
10.1016/j.peva.2004.11.009
Perform. Eval.
Keywords
Field
DocType
lower bound match,generalized processor sharing,overflow probability,sample-path large deviation,weight setting,gps weight,gaussian flow,communication networks,many-sources asymptotics,sample-path large deviations,exponential decay rate,gaussian traffic,large number,gaussian input,differentiated services,buffer size,logarithmic asymptotics,schilder’s theorem,lower bound,exponential decay,differentiated service,upper and lower bounds
Applied mathematics,Discrete mathematics,Schilder's theorem,Upper and lower bounds,Exponential decay,Real-time computing,Gaussian,Generalized processor sharing,Large deviations theory,Logarithm,Asymptotic analysis,Mathematics
Journal
Volume
Issue
ISSN
61
2-3
Performance Evaluation
Citations 
PageRank 
References 
8
0.63
18
Authors
2
Name
Order
Citations
PageRank
Michel Mandjes153473.65
Miranda Van Uitert21036.97