Abstract
This article addresses expressiveness problems for Petri nets and their useful extension for modeling and control of a system that can be modeled with Petri nets. We construct some Petri net modules, namely, an enabling module, an inhibitor module and a Modulo-N counter, which are useful for system operations. We also present the simplifications for the enabling and inhibitor modules. Then, we propose two new types of arcs, namely, enabling and inhibitor arcs, with a weighted function set. The arcs with the weighted function set from places to transitions are the marked arcs. A function set is employed to denote the weight of an arc according to the system requirements. They are very useful to solve the resource reallocation problem in a resource allocation system, where resource sharing contributes to the occurrences of deadlocks. Finally, two examples are used to show the advantages of the presented new types of arcs.
Highlights
Petri nets[1] can be served as a graphical and mathematical modeling tool for many contemporary technological systems such as flexible manufacturing systems, urban traffic systems, and concurrent programming systems
In section ‘‘Literature review,’’ we provide an overview of the related literature on several Petri net structures and compare the main features of the two proposed new net structures with them
When the sub-net contains the net structure such that there are both weighted enabling arc and weighted inhibitor arc from a place to a transition, we show that this net structure has the same enabling condition as the enabling arcs labeled by an integer interval or an integer set
Summary
Petri nets[1] can be served as a graphical and mathematical modeling tool for many contemporary technological systems such as flexible manufacturing systems, urban traffic systems, and concurrent programming systems. Some extensions to the basic Petri net structure is developed to overcome this problem by introducing extended concepts, such as enabling arcs and inhibitor arcs to control a transition enabling. In order to solve the resource reallocation problem, we first propose two novel Petri net structures, called an enabling arc with a weighted function set and an inhibitor arc with a weighted function set, respectively. Transition t is enabled by p at a marking M if M(p) is not equal to any value of the weighted function in the function set Based on these two novel arcs, we present some examples to show their applications and advantages. Section ‘‘Example’’ gives two examples and uses the new types of arcs proposed in this article to solve the problem of conflict.
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