Abstract
In this paper we present a representation of the Markov process underlying a PEP A model in terms of a Kronecker product of terms. Whilst this representation is similar to previous representations of Stochastic Automata Networks and Stochastic Petri Nets, it has novel features, arising from the definition of the PEPA models. In particular, capturing the correct timing behaviour of cooperating PEPA activities relies on functional dependencies.
This work is supported by CNRS/RS project (UIIVV 78171) and EPSRC project COMPA (G/L10215).
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References
Ajmone Marsan, A., Conte, G., Balbo, G.: A class of generalised stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems 2(2) (1984) 93–122
Bernardo, M., Gorrieri, R.: A Tutorial on EMPA: A theory of concurrent processes with nondeterminism, probabilities and time. Theoretical Computer Science. 201 (1998) 1–54
Buchholz, B.: Compositional analysis of a Markovian Process Algebra. Proc. of 2nd Process Algebra and Performance Modelling Workshop. In U. Herzog and M. Rettelbach Editors (1994)
Buchholz, P., Kemper, P.: Numerical analysis of stochastic marked graphs. Proc. of Int. Workshop on Petri Nets and Performance Models. IEEE-Computer Society Press. Durham, NC (1995) 32–41
Campos, J., Donatelli, S., Silva, M.: Structured solution of stochastic DSSP systems. Proc. of Int. Workshop on Petri Nets and Performance Models. IEEE Computer Society Press. St Malo, France (1997) 91–100
Ciardo, G., Miner, A.S.: A data structure for the efficient Kronecker solution of GSPNs. In P. Buchholz editor, Proc. of the 8th International Workshop on Petri Nets and Performance Models (PNPM’99) Zaragoza, Spain, (1999) 22–31
Clark, G., Gilmore, S., Hillston, J., Thomas, N.: Experiences with the PEPA performance modelling tools. IEE Software. 146(1) (1999) 11–19
Donatelli, S.: Superposed Generalised stochastic Petri nets: definition and efficient solution. Proc. of 15th Int. Conf. on Application and Theory of Petri Nets. In M. Silva Editor (1994)
El-Rayes, A.: Analysing performance of open queueing systems with stochastic process algebra. University of Birmingham (2000)
Fernandes, P., Plateau, B., Stewart, W.J.: Efficient vector-descriptor multiplications in stochastic automata networks. INRIA Report #2935. Anonymous ftp. http://www.ftp.inria.fr/INRIA/Publication/RR
Graham, A.: Kronecker products and matrix calculus with applications. Prentice Hall (1989)
Hermanns, H.: Interactive Markov Chains. PhD Thesis, Universität Erlangen-Nürnberg (1999)
Hermanns, H., Meyer-Kayser, J., Siegle, M.: Multi-terminal binary decision diagrams to represent and analyse continuous time Markov chains. Proc. 3rd Int. Workshop on Numerical Solution of Markov Chain, Zaragoza, Spain, (1999) 188–207
Hillston, J.: A Compositional approach to performance modeling. PhD Thesis, The University of Edinburgh (1994)
Hillston, J., Kloul, L.: From SAN to PEPA: A technology transfer. Submitted.
Molloy, M.K.: Performance analysis using stochastic Petri nets. IEEE Transactions on Computers 31(9) (1982) 913–917
Plateau, B.: On the stochastic structure of parallelism and synchronisation models for distributed algorithms. Proc. ACM Sigmetrics Conference on Measurement and Modelling of Computer Systems (1985)
Plateau, B.: De l’évolution du parallélisme et de lasync hronisation. PhD Thesis, Université de Paris-Sud, Orsay (1984)
Rettelbach, M., Siegle, M.: Compositional minimal semantics for the stochastic process algebra TIPP. Proc. of 2nd Workshop on Process Algebra and Performance Modelling (1994)
Sanders, W.H., Meyer, J.F.: Reduced base model construction methods for stochastic activity networks. IEEE Journal on Selected Areas in Communications 9(1) (1991) 25–36
Stewart, W.J., Atif, K., Plateau, B.: The numerical solution of stochastic automata networks. European Journal of Operations Research 86(3) (1995) 503–525
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Hillston, J., Kloul, L. (2001). An Efficient Kronecker Representation for PEPA Models. 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_8
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DOI: https://doi.org/10.1007/3-540-44804-7_8
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