Timed Petri nets definitions, properties, and applications

Abstract

In timed Petri nets, the transitions fire in “real-time”, i.e., there is a (deterministic or random) firing time associated with each transition, the tokens are removed from input places at the beginning of firing, and are deposited into output places when the firing terminates (they may be considered as remaining “in” the transitions for the firing time). Any “state” description of timed nets must thus take into account the distribution of tokens in places as well as in (firing) transitions, and the state space of timed nets can be quite different from the space of reachable markings. Performance analysis of timed nets is based on stationary probabilities of states. For bounded nets stationary probabilities are determined from a finite set of simultaneous linear equilibrium equations. For unbounded nets the state space is infinite, the set of linear equilibrium equations is also infinite and it must be reduced to a finite set of nonlinear equations for effective solution. Simple examples illustrate capabilities of timed Petri net models.