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6897 Uniformization with Representatives - comprehensive transient analysis of infinite-state QBDs

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Remke, A.K.I. and Haverkort, B.R.H.M. and Cloth, L. (2006) Uniformization with Representatives - comprehensive transient analysis of infinite-state QBDs. In: First International Conference on Performance Evaluation Methodologies and Tools, 10 Oct 2006, Pisa, Italy. 7. ACM. ISBN 1-59593-506-1

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Official URL: http://doi.acm.org/10.1145/1190366.1190372

Abstract

A large variety of computer and communication systems can be modeled adequately as infinite-state continuous-time Markov chains (CTMCs). A highly structured class of such infinite-state CTMCs is the class of Quasi-Birth-Death processes (QBDs), on which we focus in this paper. We present an efficient variant of uniformization for computing the transient probability $\mathbf{V}_{i,j}(t)$ of being in each state $j$ of the QBD for any possible initial state $i$ at time $t$ . Note that both the set of starting states and the set of goal states have infinite size. All the probabilities $\mathbf{V}_{i,j}(t)$ are needed in the context of probabilistic model checking. The key idea of our algorithm is to split the infinite set of starting states into a finite part and an infinite (repeating) part. The transient probabilities for the infinite part are then computed using the new notion of $\emph{representatives}$ . We present the required data structures and algorithm, as well as an application-dependent optimal stopping criterion. In
a simple case study we show the feasibility of our approach, as well as the efficiency gain due to the optimal stopping criterion.

Item Type:	Conference or Workshop Paper (Full Paper, Talk)
Research Group:	EWI-DACS: Design and Analysis of Communication Systems
Research Program:	CTIT-UBRICKS: Building Blocks for Ubiquitous Computing and Communication
Research Project:	MC=MC: Model-Checking of Infinite-State Markov Chains, MOQS: Modeling and Analysis of QoS of Component-Based Designs
ID Code:	6897
Status:	Published
Deposited On:	24 October 2006
Refereed:	Yes
International:	Yes
More Information:	statistics metis

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