By William J. Stewart (auth.), Marco Bernardo, Jane Hillston (eds.)
This booklet provides a collection of eleven papers accompanying the lectures of top researchers given on the seventh variation of the foreign college on Formal tools for the layout of laptop, verbal exchange and software program structures, SFM 2007, held in Bertinoro, Italy in May/June 2007.SFM 2007 used to be dedicated to formal innovations for functionality assessment and coated a number of facets of the sector, together with formalisms for functionality modeling (Markov chains, queueing networks, stochastic Petri nets, and stochastic approach algebras), equivalence checking and version checking, effective resolution concepts, and software program functionality engineering.
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Extra info for Formal Methods for Performance Evaluation: 7th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2007, Bertinoro, Italy, May 28-June 2, 2007, Advanced Lectures
However, for modeling purposes this can be a constraint that should often be relaxed. We shall now introduce a class of quite general distributions used in the analysis of QNs. Coxian distributions are deﬁned as a linear combination of exponential variables, and can be represented by a network of exponential stages. 3. A second reason is that Coxian distribution has a rational Laplace transform and can approximate any distribution arbitrarily closely . Queueing Networks 45 Fig. 2. A queueing system with a Coxian server with L stages Figure 2 illustrates a queueing system whose service time is modeled by a Coxian distribution with L exponential stages.
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63] Y. Saad. Numerical methods for large eigenvalue problems. John Wiley & Sons, Manchester Univ. Press, 1992.  I. Sbeity, B. Plateau, L. J. Stewart. Phase-Type Distributions in Stochastic Automata Networks. To appear in European Journal of Operations Research. J. Schweitzer. Aggregation methods for large Markov chains. In Mathematical Computer Performance and Reliability, G. J. Courtois and A. Hordijk, Eds. North-Holland, Amsterdam, pp 275–286, 1984.  P. Semal. Two bounding schemes for the steady state solution of Markov chains.