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Tail Asymptotics for Monotone-Separable Networks

Part of:Special processesLimit theorems

Published online by Cambridge University Press:  14 July 2016

Marc Lelarge
Marc Lelarge*
Affiliation:
University College Cork
*
∗ Current address: ENS-INRIA, 45 rue d'Ulm, 75005 Paris, France. Email address: marc.lelarge@ens.fr
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Abstract

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A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

Keywords

Large deviationqueueing network

MSC classification

Primary:60F10: Large deviations
Secondary:60K25: Queueing theory

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007, pp. 306 - 320
Copyright
Copyright © Applied Probability Trust 2007 

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