Insensitivity to service-time distributions for fluid queueing models

Tschaikowski, Max and Tribastone, Mirco Insensitivity to service-time distributions for fluid queueing models. In: 7th International Conference on Performance Evaluation Methodologies and Tools, December 10–12, 2013, Turin, Italy pp. 273-281. ISBN 978-1-936968-48-0. (2013)

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Abstract

We study fluid limits based on ordinary differential equations (ODEs) for Markovian queueing models where nonexponential service times are fit by appropriate Coxian distributions to match their first and second moments. We focus on a heavy-load regime, whereby the fluid limit of the queue-length process of the nonexponential queue estimates a bottleneck situation. Under this condition, we show that the ODE solution admits a steady state which is insensitive to the service-time distribution: The ODE steady state only depends on the mean service times. By contrast, the steady-state average performance measures computed by Markovian analysis are in general dependent on the higher-order moments of the service-time distribution. A numerical investigation shows that, given any two Markovian queueing models with Coxian-distributed service times with the same mean and different variance, the model with lower variance converges more rapidly to the (same) fluid limit than the one with higher variance.

Item Type: Conference or Workshop Item (Paper) 10.4108/icst.valuetools.2013.254374 Q Science > QA Mathematics > QA75 Electronic computers. Computer science Computer Science and Applications Caterina Tangheroni 27 Jul 2015 08:02 27 Jul 2015 08:02 http://eprints.imtlucca.it/id/eprint/2734