×

zbMATH — the first resource for mathematics

Fluid stochastic Petri nets: Theory, applications, and solution techniques. (English) Zbl 0957.90011
Summary: 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.

MSC:
90B10 Deterministic network models in operations research
90C40 Markov and semi-Markov decision processes
Software:
SPNP
PDF BibTeX Cite
Full Text: DOI
References:
[1] Marsan, M.Ajmone; Balbo, G.; Conte, G., Performance models of multiprocessor systems, (1986), MIT Press Cambridge, MA
[2] Marsan, M.Ajmore; Chiola, G., On Petri nets with deterministic and exponentially distributed firing times, (), 132-145
[3] Anick, D.; Mitra, D.; Sondhi, M., Stochastic theory of data-handling systems, Bell system technical journal, 61, 8, 1871-1894, (1982)
[4] Axelsson, O., A class of A-stable methods, Bit, 9, 185-199, (1969) · Zbl 0208.41504
[5] Bank, R.E.; Coughran, W.M.; Fichtner, W.; Grosse, E.H.; Rose, D.J.; Smith, R.K., Transient simulation of silicon devices and circuits, IEEE transactions on computer-aided design, 4, 436-451, (1985)
[6] Cassandras, C.G., Discrete event systems: modeling and performance analysis, (1993), Aksen Associates Holmwood, IL
[7] Ciardo, G.; Muppala, J.K.; Trivedi, K.S., SPNP: stochastic Petri net package, (), 142-150
[8] Ciardo, G.; Blakemore, A.; Chimento, P.F.J.; Muppala, J.K.; Trivedi, K.S., Automated generation and analysis of Markov reward models using stochastic reward nets, () · Zbl 0799.60085
[9] Ciardo, G.; Muppala, J.K.; Trivedi, K.S., Analyzing concurrent and fault-tolerant software using stochastic Petri nets, Journal of parallel and distributed computing, 15, 3, 255-269, (1992)
[10] Cinlar, E., Introduction to stochastic processes, (1975), Prentice-Hall Englewood Cliffs, NJ · Zbl 0341.60019
[11] Elwalid, A.I.; Mitra, D., Statistical multiplexing with loss priorities in rate-based congestion control of high-speed networks, IEEE transactions on communications, 42, 11, 2989-3002, (1994)
[12] Iyer, R.K.; Rosetti, D.J.; Hsueh, M.C., Measurement and modeling of computer reliability as affected by system activity, ACM transactions on computer systems, 4, 214-237, (1986)
[13] Karandikar, R.J.; Kulkarni, V.G., Second-order fluid flow models: reflected Brownian motion in a random environment, Operations research, 43, 1, 77-88, (1995) · Zbl 0821.60087
[14] Mitra, D., Stochastic theory of fluid models of multiple failure-susceptible producers and consumers coupled by a buffer, Advances in applied probability, 20, 646-676, (1988) · Zbl 0656.60079
[15] Murata, T., Petri nets: properties, analysis and applications, (), 541-579, (4)
[16] Patankar, S.V., Numerical heat transfer and fluid flow, (1980), McGraw-Hill New York · Zbl 0595.76001
[17] Peterson, J.L., Petri net theory and the modeling of systems, (1981), Prentice-Hall Englewood Cliffs, NJ
[18] Robertazzi, T., Computer networks and systems: queueing theory and performance evaluation, (1990), Springer-Verlag New York · Zbl 0729.68005
[19] Trivedi, K.S.; Kulkarni, V.G., FSPNs: fluid stochastic Petri nets, (), 24-31
[20] Viswanadham, N.; Narahari, Y., Performance modeling of automated manufacturing systems, (1992), Prentice-Hall Englewood Cliffs, NJ · Zbl 0800.90541
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.