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A Bayesian Approach to Parameter Inference in Queueing Networks

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http://dl.acm.org/citation.cfm?id=2893480
Original languageEnglish
Article number2
Number of pages26
JournalACM Transactions on Modeling and Computer Simulation
Volume27
Issue number1
DOIs
Publication statusPublished - Aug 2016

Abstract

The application of queueing network models to real-world applications often involves the task of estimating the service demand placed by requests at queueing nodes. In this paper, we propose a methodology to estimate service demands in closed multi-class queueing networks based on Gibbs sampling. Our methodology requires measurements of the number of jobs at resources and can accept prior probabilities on the demands.
Gibbs sampling is challenging to apply to estimation problems for queueing networks since it requires to efficiently evaluate a likelihood function on the measured data. This likelihood function depends on the equilibrium solution of the network, which is difficult to compute in closed models due to the presence of the normalizing constant of the equilibrium state probabilities. To tackle this obstacle, we define a novel iterative approximation of the normalizing constant and show the improved accuracy of this approach, compared to existing methods, for use in conjunction with Gibbs sampling. We also demonstrate that, as a demand estimation tool, Gibbs sampling outperforms other popular Markov Chain Monte Carlo approximations.Experimental validation based on traces from a cloud application demonstrates the effectiveness of Gibbs sampling for service demand estimation in real-world studies.

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