Abstract
Several semantics models are adopted by time Petri nets for different applications. Yet they have some limitations on schedulability analysis of flexible manufacturing systems. The scheduling scope of a strong semantics model is greatly limited because of the impact of strong timing requirements, perhaps keeping some optimal schedules out of the consideration. A weak semantics model cannot guarantee the scheduling timeliness as there lacks strong timing enforcement. A mixed semantics model cannot ensure that independent transitions with overlapping firing interval fire in an interleaving way, thus affecting the search for the optimal schedules. In this paper, we present a relaxed mixed semantics model for time Petri nets to address these problems by redefining the firability rules of transitions. In our model, the firability of a transition is determined by maximal concurrent sets containing the transition. This treatment not only extends the scheduling scope of TPN model greatly while avoiding the generation of invalid schedules, but also solves the problem of concurrent scheduling of independent transitions. A state class method is then proposed to support the verification and analysis of temporal properties. Finally, we apply the proposed model to schedulability analysis of a job shop scheduling problem, and compare the features of four semantics models.
Highlights
Petri nets as a mathematical tool, have been widely used to handle many problems in discrete event systems [1]–[4]
STRONG SEMANTICS MODELS To describe different semantics models of time Petri nets in a uniform way, we introduce the concepts of time bound and efficient firing interval
In a time Petri net with strong semantics (S-time Petri nets (TPNs)), an enabled transition t is firable at state s if
Summary
Petri nets as a mathematical tool, have been widely used to handle many problems in discrete event systems [1]–[4]. In a time Petri net with strong semantics (S-TPN), an enabled transition t is firable at state s if. C. WEAK SEMANTICS MODELS In a time Petri net with weak semantics (W-TPN), enabled transition t is firable at state s if. In a time Petri net with mixed semantics (M-TPNs), progressive enabled transition t is firable at state s if max(↓ f (t), 0) ≤ ↑f (ti) for any ti ∈ En(M − B(t)). The efficient firing time bound of firable transition t at state s is defined as (t) = max{↑U |U ∈ U(M , t)}. Property 3 shows that RM-TPNs can keep the consistency of the non-emptiness of the enabled and firable transition sets at any state. Property 4 shows that two independent transitions with overlapping efficient firing intervals in a maximal concurrent set can fire independently in an RM-TPN. They cannot fire in an interleaving way from s0
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