Fluid stochastic Petri nets: Theory,applications, and solution techniques |
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| Affiliation: | 1. Lehrstuhl für Rechnerstrukturen (IMMD 3), Universität Erlangen-Nürnberg, Martensstraße 3, 91 058 Erlangen, Germany;2. Department of Operations Research, University of North Carolina, Chapel Hill, NC 27 599, USA;3. Department of Computer Science, College of William and Mary, Williamsburg, VA 23 187-8795, USA;4. Center for Advanced Computing and Communication, Department of Electrical and Computer Engineering, Duke University, Durham, NC 27 708-0291, USA;1. Department of Theory of Functions, Institute of Applied Mathematics and Mechanics of NASU, Dobrovolskogo str. 1, Slovyansk 84100, Ukraine;2. Department of Applied Mechanics, Institute of Applied Mathematics and Mechanics of NASU, Dobrovolskogo str. 1, Slovyansk 84100, Ukraine;1. University of Oxford, United Kingdom;2. Queen Mary University of London, United Kingdom;1. Fachbereich Mathematik, TU Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany;2. Département d’Informatique, Université Libre Du Bruxelles, ULB CP212, Boulevard du Triomphe, 1050 Bruxelles, Belgium |
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| Abstract: | In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented and evidence of the accuracy of the fluid approximation is given. |
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