Fluid stochastic Petri nets: Theory, applications, and solution techniques.

*(English)*Zbl 0957.90011Summary: 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
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\textit{G. Horton} et al., Eur. J. Oper. Res. 105, No. 1, 184--201 (1998; Zbl 0957.90011)

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##### References:

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