Abstract
Markovian behavioral equivalences can be exploited for state space reduction before performance evaluation takes place. It is known that Markovian bisimilarity corresponds to ordinary lumpability and that Markovian testing and trace equivalences correspond to a coarser exact relation we call T-lumpability. While there exists an ordinary-lumpability-consistent aggregation algorithm, this is not the case with T-lumpability. Based on the axiomatization of Markovian testing and trace equivalences, we provide a sufficient condition for T-lumpability that can easily be embedded in the aggregation algorithm for ordinary lumpability, thus enhancing the potential for exact state space reduction. We also identify a class of systems – those providing incremental services – for which the resulting aggregation algorithm turns out to be useful.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bernardo, M.: “Non-Bisimulation-Based Markovian Behavioral Equivalences”. Journal of Logic and Algebraic Programming 72, 3–49 (2007)
Bernardo, M.: A Survey of Markovian Behavioral Equivalences. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 180–219. Springer, Heidelberg (2007)
Buchholz, P.: Exact and Ordinary Lumpability in Finite Markov Chains. Journal of Applied Probability 31, 59–75 (1994)
Cleaveland, R., Hennessy, M.: Testing Equivalence as a Bisimulation Equivalence. Formal Aspects of Computing 5, 1–20 (1993)
Derisavi, S., Hermanns, H., Sanders, W.H.: Optimal State-Space Lumping in Markov Chains. Information Processing Letters 87, 309–315 (2003)
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)
Paige, R., Tarjan, R.E.: Three Partition Refinement Algorithms. SIAM Journal on Computing 16, 973–989 (1987)
Wolf, V., Baier, C., Majster-Cederbaum, M.: Trace Machines for Observing Continuous-Time Markov Chains. In: Proc.of the 3rd Int. Workshop on Quantitative Aspects of Programming Languages (QAPL 2005), Edinburgh, UK. ENTCS, vol. 153(2), pp. 259–277 (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bernardo, M. (2008). Towards State Space Reduction Based on T-Lumpability-Consistent Relations. In: Thomas, N., Juiz, C. (eds) Computer Performance Engineering. EPEW 2008. Lecture Notes in Computer Science, vol 5261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87412-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-87412-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87411-9
Online ISBN: 978-3-540-87412-6
eBook Packages: Computer ScienceComputer Science (R0)