Abstract
We consider a discrete time process algebra capable of (i) modeling processes with different probabilistic advancing speeds (mean number of actions executed per time unit), and (ii) expressing probabilistic external/internal choices and multiway synchronization. We show that, when evaluating steady state based performance measures expressed by associating rewards with actions, such a probabilistic approach provides an exact solution even if advancing speeds are considered not to be probabilistic (i.e. actions of different processes have a different exact duration), without incurring in the state space explosion problem which arises with an intuitive application of a standard synchronous approach. We then present a case study on multi-path routing showing the expressiveness of our calculus and that it makes it particularly easy to produce scalable specifications.
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References
A. Aldini, M. Bravetti, “An Asynchronous Calculus for Generative-Reactive Probabilistic Systems”, in Proc. of 8th Int. Workshop on Process Algebra and Performance Modeling, pp. 591–605, 2000
M. Bravetti, A. Aldini, “An Asynchronous Calculus for Generative-Reactive Probabilistic Systems”, Tech. Rep. UBLCS-2000-03, Univ. Bologna, Italy, 2000
J.C.M. Baeten, J.A. Bergstra, S.A. Smolka, “Axiomatizing Probabilistic Processes: ACP with Generative Probabilities”, in Inf. and Comp. 121:234–255, 1995
M. Bernardo, “Theory and Application of Extended Markovian Process Algebra”, Ph. D. Thesis, Univ. Bologna, Italy, 1999
R.J. van Glabbeek, S.A. Smolka, B. Steffen, “Reactive, Generative and Stratified Models of Probabilistic Processes”, in Inf. and Comp. 121:59–80, 1995
C.A.R. Hoare, “Communicating Sequential Processes”, Prentice Hall, 1985
C.-C. Jou, S.A. Smolka, “Equivalences, Congruences, and Complete Axiomatizations for Probabilistic Processes”, in Proc. of 1st Int. Conf. on Concurrency Theory, LNCS 458:367–383, 1990
K.G. Larsen, A. Skou, “Compositional Verification of Probabilistic Processes”, in Proc. of 3rd Int. Conf. on Concurrency Theory, LNCS 630:456–471, 1992
R. Segala, “Modeling and Verification of Randomized Distributed Real-Time Systems”, Ph. D. Thesis, MIT, Boston (MA), 1995
A. S. Tanenbaum, “Computer Networks”, Prentice Hall, 1996
C. Tofts, “Processes with Probabilities, Priority and Time”, in Formal Aspects of Computing 6:536–564, 1994
S. H. Wu, S.A. Smolka, E.W. Stark, “Composition and Behaviors of Probabilistic I/O Automata”, in Theoretical Computer Science 176:1–38, 1997
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© 2001 Springer-Verlag Berlin Heidelberg
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Bravetti, M., Aldini, A. (2001). Expressing Processes with Different Action Durations through Probabilities. In: de Alfaro, L., Gilmore, S. (eds) Process Algebra and Probabilistic Methods. Performance Modelling and Verification. PAPM-PROBMIV 2001. Lecture Notes in Computer Science, vol 2165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44804-7_11
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DOI: https://doi.org/10.1007/3-540-44804-7_11
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