Parallel computation of response time densities and quantiles in large Markov and semiMarkov models

Abstract

Response time quantiles reflect user-perceived quality of service more accurately than mean or average response time measures. Consequently, on-line transaction process-ing benchmarks, telecommunications Service Level Agreements and emergency ser-vices legislation all feature stringent 90th percentile response time targets. This thesis presents techniques and tools for extracting response time densities, quan-tiles and moments from large-scale models of real-life systems. This work expands the applicability, capacity and specification power of prior work, which was hitherto focused on the analysis of Markov models which only support exponential delays. Response time densities or cumulative distribution functions of interest are computed by calculating and subsequently numerically inverting their Laplace transforms. We develop techniques for the extraction of response time measures from Generalised Stochastic Petri Nets (GSPNs) and Semi-Markov Stochastic Petri Nets (SM-SPNs). The latter is our proposed modelling formalism for the high-level specification of semi-Markov models which support generally-distributed delays