Timing-dependent boundedness and liveness in continuous Petri nets

The classical structural boundedness and repetitiveness properties for discrete and untimed models are reconsidered here for timed continuous Petri nets (TCPN), under infinite server semantics. The timing is also involved in the analysis, by taking advantage of its matricial characterization. Properties analogous to conservativeness and consistency, in which the timing is involved, are defined. It is shown that such properties are sufficient for timed boundedness and timed liveness, respectively, even if the untimed model does not exhibit such properties. The rest of the paper is devoted to the study of these timing-dependent boundedness and liveness.