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Ergodicity and Throughput Bounds of Petri Nets with Unique Consistent Firing Count Vector
February 1991 (vol. 17 no. 2)
pp. 117-125

Ergodicity and throughput bound characterization are addressed for a subclass of timed and stochastic Petri nets, interleaving qualitative and quantitative theories. The nets considered represent an extension of the well-known subclass of marked graphs, defined as having a unique consistent firing count vector, independently of the stochastic interpretation of the net model. In particular, persistent and mono-T-semiflow net subclasses are considered. Upper and lower throughput bounds are computed using linear programming problems defined on the incidence matrix of the underlying net. The bounds proposed depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). From a different perspective, the considered subclasses of synchronized queuing networks; thus, the proposed bounds can be applied to these networks.

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Index Terms:
persistent nets; ergodicity; throughput bounds; Petri nets; unique consistent firing count vector; marked graphs; mono-T-semiflow net subclasses; linear programming; incidence matrix; synchronized queuing networks; linear programming; Petri nets
Citation:
J. Campos, G. Chiola, M. Silva, "Ergodicity and Throughput Bounds of Petri Nets with Unique Consistent Firing Count Vector," IEEE Transactions on Software Engineering, vol. 17, no. 2, pp. 117-125, Feb. 1991, doi:10.1109/32.67593
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