Behaviour equivalent max-plus automata for timed petri nets under open-loop race-policy semantics

Timed Petri nets and max-plus automata are well known modelling frameworks for timed discrete-event systems. In this paper we present an iterative procedure that constructs a max-plus automaton from a timed Petri net while retaining the timed behaviour. Regarding the Petri net, we essentially impose three assumptions: (a) the Petri net must be bounded, i.e, the reachability graph must be finite; (b) we interpret the Petri net with single server semantics; and (c) the Petri net operates according to the race policy, i.e., the earliest possible transition will fire and thereby possibly consume tokens required by other competing transitions. Under these assumptions we show that the proposed procedure terminates with a finite deterministic max-plus automaton that realises the same timed behaviour as the Petri net. As a variation of the plain race policy, we also consider that a subsequently designed supervisor may temporarily disable distinguished transitions. Again, we present a terminating procedure that constructs a behaviour equivalent deterministic max-plus automaton. We demonstrate by example how the latter automaton can be utilised as an open-loop model in the context of supervisor control.