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Response Time Densities and Quantiles in Large Markov and Semi-Markov Models

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Title: Response Time Densities and Quantiles in Large Markov and Semi-Markov Models
Authors: Bradley, J
Dingle, N
Harder, U
Harrison, P
Knottenbelt, W
Item Type: Chapter
Abstract: Response time quantiles reflect user-perceived quality of service more accurately than mean or average response time measures. Consequently, on-line transaction processing benchmarks, telecommunications Service Level Agreements and emergency services legislation all feature stringent 90th percentile response time targets. This chapter describes a range of techniques for extracting response time densities and quantiles from large-scale Markov and semi-Markov models of real-life systems. We describe a method for the computation of response time densities or cumulative distribution functions which centres on the calculation and subsequent numerical inversion of their Laplace transforms. This can be applied to both Markov and semi-Markov models. We also review the use of uniformization to calculate such measures more efficiently in purely Markovian models. We demonstrate these techniques by using them to generate response time quantiles in a semi-Markov model of a high-availability web-server. We show how these techniques can be used to analyse models with state spaces of 10^7 states and above.
Issue Date: 31-Dec-2006
URI: http://hdl.handle.net/10044/1/5845
Publisher Link: https://www.novapublishers.com/catalog/product_info.php?cPath=23_29&products_id=4012
ISBN: 1-59454-817-X
Publisher: Nova Science Publishers, Inc
Presented At: Performance Evaluation of Parallel, Distributed and Emergent Systems
Start Page: 3
End Page: 41
Copyright Statement: © 2003 Nova Science Publishers Inc.
Appears in Collections:High Performance Informatics