Clarifying the priority specification of GSPN: Detached priorities

Abstract

The global multilevel priority de nition in GSPN, while being most convenient with many respects, poses some modelling problems related with confusion and indirect con icts, which may lead to undesired e ects in the de nition of the underlying stochastic process. While some of these problems have been recognized and dealt with in previous works on the de nition of GSPN, through the introduction of extended c on ict sets, some others, that will be illustrated in this paper, were not covered. To overcome all these problems, in this paper a syntactical subclass of GSPN, called detached priorities GSPN dpGSPN, is proposed. In dpGSPN no confusion or indirect con icts are p ossible, and according to our experience, modelling power is not substantially sacri ced. To facilitate the modelling, a possible method to derive a suitable global priority de nition from local information is outlined.

Practical Use of High-level Petri Nets

“…Thus a reservation is torn down in both the router and the sender (event no 18). Following that, the receiver sends a resv refresh, which propagates to the sender and reestablishes the reservation state on both the router and sender host (event no [19][20][21][22]. Finally, the sender application finishes a session using a RelSender call, and the sender sends a PathTear message which will propagate to the receiver (event no 23-25).…”

“…The weight function w is handled similarly to the priority o n e . W e assume that there are not marking dependent w eights and rates, and we basically leave the user the task of rede ning pri and w for the nal net, since compositional ways to handle pri and w are still an open question, although some attempts to address this problem may be found in 16,21]. The operation to superpose places is the direct counterpart of the operation described above, with the additional, obvious, constraint, that places of equal label should have the same colour domain.…”

Well-defined generalized stochastic petri nets: a net-level method to specify priorities

“…This approach has been followed extensively and is incorporated in most tools because it exhibits the two appealing features of net-level, or structural, reasoning: efficiency because it works on the net, not on the state space, and robustness, that means that, typically, the correct model is correct for "any" property that we might want to analyze, and it is still correct if we change the timing and probabilities information, and even, to some extent, the initial state. Unfortunately, it was found recently [20] that the current net-level definition of GSPN is not complete, in the sense that there is a (somehow weird) situation that it does not take into account.…”

“…. In [20], we proposed a net-level restriction to the priority specification to prevent the problems, by using a subclass of nets were they cannot appear.…”

“…The "subclasses approach" had not been generally advised, due to the fact that topological subclasses being confusion free (e.g., free choice nets) are very limited from a modeling point of view, namely, to model mutual exclusion in the access to shared resources [7]. Nevertheless, in [20], completely general net topologies are allowed, only the priorities are restricted so that immediate transitions not intended to be in effective conflict have different priorities, hence only the firing of transitions which are intended to be in conflict need a probabilistic specification. This leads to the class of detached priorities GSPN, which cannot exhibit stochastic confusion or indirect conflicts, what was considered a desired feature.…”