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Properties and Performance Bounds for Timed Marked Graphs.

Campos, Javier; Chiola, Giovanni; Colom, José Maria; Silva, Manuel

Technical Report GISI--RR--90--17. Universidad de Zaragoza (Spain), Dpto. Ingeniería Eléctrica e Informática, Grupo Ing. de Sistemas Informática, July 1990.

Abstract: A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called timed marked graphs. Ergodicity is derived from boundedness and liveness of the underlying Petri net representation. The problem of computing upper and lower bounds for the steady-state performance of timed and stochastic marked graphs is studied. Linear programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight bounds for the throughput of transitions. The aim of the paper is to show the benefits of interleaving qualitative and quantitative analysis of Petri net models.

Keywords: steady-state performance (of) timed stochastic marked graph(s) synchronized queueing network (with) deterministic routing; timed net; ergodicity; boundedness; liveness; linear programming; transition throughput.

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