eprintid: 2602
rev_number: 5
eprint_status: archive
userid: 6
dir: disk0/00/00/26/02
datestamp: 2015-02-11 14:17:18
lastmod: 2015-02-11 14:17:18
status_changed: 2015-02-11 14:17:18
type: article
metadata_visibility: show
creators_name: Tribastone, Mirco
creators_name: Ding, Jie
creators_name: Gilmore, Stephen
creators_name: Hillston, Jane
creators_id: mirco.tribastone@imtlucca.it
creators_id: 
creators_id: 
creators_id: 
title: Fluid rewards for a stochastic process algebra
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Markov processes; Modeling and prediction; ordinary differential equations

abstract: Reasoning about the performance of models of software systems typically entails the derivation of metrics such as throughput, utilization, and response time. If the model is a Markov chain, these are expressed as real functions of the chain, called reward models. The computational complexity of reward-based metrics is of the same order as the solution of the Markov chain, making the analysis infeasible when evaluating large-scale systems. In the context of the stochastic process algebra PEPA, the underlying continuous-time Markov chain has been shown to admit a deterministic (fluid) approximation as a solution of an ordinary differential equation, which effectively circumvents state-space explosion. This paper is concerned with approximating Markovian reward models for PEPA with fluid rewards, i.e., functions of the solution of the differential equation problem. It shows that (1) the Markovian reward models for typical metrics of performance enjoy asymptotic convergence to their fluid analogues, and that (2) via numerical tests, the approximation yields satisfactory accuracy in practice.
date: 2012-07
date_type: published
publication: IEEE Transactions on Software Engineering
volume: 38
number: 4
publisher: IEEE Computer Society
pagerange: 861-874
id_number: 10.1109/TSE.2011.81
refereed: TRUE
issn: 0098-5589
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5975178&isnumber=6249691
citation:   Tribastone, Mirco and Ding, Jie and Gilmore, Stephen and Hillston, Jane  Fluid rewards for a stochastic process algebra.  IEEE Transactions on Software Engineering, 38 (4).  pp. 861-874.  ISSN 0098-5589      (2012)