Abstract
In this paper we present product-form solutions from the point of view of stochastic process algebra. In previous work [16] we have shown how to derive product-form solutions for a formalism called Labelled Markov Automata (LMA). LMA are very useful as their relation with the Continuous Time Markov Chains is very direct. The disadvantage of using LMA is that the proofs of properties are cumbersome. In fact, in LMA it is not possible to use the inductive structure of the language in a proof. In this paper we consider a simple stochastic process algebra that has the great advantage of simplifying the proofs. This simple language has been inspired by PEPA [10], however, detailed analysis of the semantics of cooperation will show the differences between the two formalisms. It will also be shown that the semantics of the cooperation in process algebra influences the correctness of the derivation of the product-form solutions.
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References
Anderson, D., Craciun, G., Kurtz, T.: Product-form stationary distributions for deficiency zero chemical reaction networks. Bulletin of Mathematical Biology 72, 1947–1970 (2010)
Balbo, G., Bruell, S.C., Sereno, M.: Product form solution for Generalized Stochastic Petri Nets. IEEE Trans. on Software Eng. 28, 915–932 (2002)
Balbo, G., Bruell, S.C., Sereno, M.: On the relations between BCMP Queueing Networks and Product Form Solution Stochastic Petri Nets. In: Proc. of 10th Int. Workshop on Petri Nets and Performance Models, pp. 103–112 (2003)
Boucherie, R.J.: A characterisation of independence for competing Markov chains with applications to stochastic Petri nets. IEEE Tran. on Software Eng. 20(7), 536–544 (1994)
Chao, X., Miyazawa, M., Pinedo, M.: Queueing Networks. John Wiley & Sons Ltd. (1999)
Clark, G., Hillston, J.: Product form solution for an insensitive stochastic process algebra structure. Performance Evaluation 50, 129–151 (2002)
Coleman, J.L., Henderson, W., Taylor, P.G.: Product form equilibrium distributions and a convolution algorithm for Stochastic Petri nets. Perform. Eval. 26, 159–180 (1996)
Harrison, P., Hillston, J.: Exploiting quasi-reversible structures in Markovian process algebra models. The Computer Journal 38(7), 510–520 (1995)
Harrison, P.G.: Turning back time in Markovian process algebra. Theoretical Computer Science 290(3), 1947–1986 (2003)
Hillston, J.: A Compositional Approach to Perfomance Modelling. PhD thesis, Department of Computer Science, Edinburgh (1994)
Hillston, J., Thomas, N.: Product Form Solution for a class of PEPA Models. In: Proceedings of IEEE International Computer Performance and Dependability Symposium, Durham, NC (September 1998); An extended version appeared in Performance Evaluation 35(3-4) (1999)
Hillston, J., Thomas, N.: Product form solution for a class of PEPA models. Perform. Eval. 35(3-4), 171–192 (1999)
Hillston, J.: A class of PEPA models exhibiting product form solution over submodels. Technical Report ECS-LFCS-98-382, University of Edingburgh (February 1998)
Kelly, F.P.: Reversibility and Stochastic Networks. Wiley (1979)
Mairesse, J., Nguyen, H.-T.: Deficiency Zero Petri Nets and Product Form. In: Franceschinis, G., Wolf, K. (eds.) PETRI NETS 2009. LNCS, vol. 5606, pp. 103–122. Springer, Heidelberg (2009)
Marin, A., Vigliotti, M.G.: A general result for deriving product-form solutions in Markovian models. In: Proceedings of First Joint WOSP/SIPEW International Conference on Performance Engineering (January 2010)
Milner, R.: Communicating and Mobile Systems: the π-calculus. Cambridge University Press (1999)
Thomas, G.: Robertazzi. In: Computer Networks and Systems. Springer (1994)
Sereno, M.: Towards a product form solution for stochastic process algebras. The Computer Journal 38(7), 622–632 (1995)
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Vigliotti, M.G. (2013). Operational Semantics for Product-Form Solution. In: Tribastone, M., Gilmore, S. (eds) Computer Performance Engineering. EPEW UKPEW 2012 2012. Lecture Notes in Computer Science, vol 7587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36781-6_2
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DOI: https://doi.org/10.1007/978-3-642-36781-6_2
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