Petri Net Marking Research Articles

Analysis of Deadlock and Circular Waits Using a Matrix Model for Flexible Manufacturing Systems

The problem of deadlock in a large class of reentrant flowline systems is analysed based on a Petri net model. The relation between deadlock and circular waits is established by rigorously defining the situation of circular blocking. Deadlock analysis is then performed in terms of circular waits and their associated structures, the so-called critical siphons and critical subsystems. A dynamical system representation obtained by coupling the Petri net marking transition equation with the matrix rule-based controller equations is adopted. The task of computing the Petri net structures of deadlock analysis is largely simplified (operations involved are of polynomial complexity) by using the matrices of this system description. An on-line maximally permissive control policy for deadlock avoidance (MAXWIP) is then devised. This can be efficiently implemented by incorporating the “outer-loop” control decisions via certain dispatching control inputs. The result is a dispatching control with deadlock avoidance, which is a generalized kanban scheme.

A new matrix model for discrete event systems: application to simulation

Simulation schemes for discrete event (DE) systems based on a new DE matrix formulation are presented. This new formulation is a hybrid system with logical and algebraic components that allows fast, direct design and reconfiguration of rule-based controllers for manufacturing systems. It applies to general DE systems that include shared resources, dispatching, circular waits, and variable part routing. A certain DE matrix state equation together with the familiar Petri net marking transition equation yield a complete dynamical description of a DE system. Our goal in this article is to show that this provides a simplified computer tool that allows efficient simulation and modeling for DE systems.

Petri Nets, Commutative Context-Free Grammars, and Basic Parallel Processes

The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NP-complete. Further consequences are: the uniform word problem for commutative context-free grammars is NP-complete; weak-bisimilarity is semidecidable for Basic Parallel Processes.

Efficient computerized Petri net approach for the enumeration of the sets of path identifiers for reliability analysis of broadcasting networks

An efficient Petri net approach for enumerating the sets of path identifiers for the reliability analysis of broadcasting networks is presented. The sets of path identifiers are enumerated with the help of a place-to-transilion incident matrix of the Petri net model of Ihe given network. The reachability, marking and firing concepts of Petri nets are used to give a Petri net interpretation to certain properties of the network. The proposed method is applicable to ST-connectivity, SKT-connectivity and SAT-connectivity problems. The sets of path identifiers are generated in ascending order of cardinality which is one of the basic requirements for efficiency in most of the techniques available for obtaining the symbolic and numerical system reliability expressions. The developed algorithm has been programmed in FOR-TRAN-77 and tested on various types of data. The proposed method directly obtains the sels of path identifiers for SKT- and SAT-connectivity problems without the necessity of generating the ST-minimal path sets. In comparison to the previously published approach, the algorithm is conceptually simpler and requires less computer time and memory space. Examples have been provided to demonstrate the effectiveness of the method. A comparison of CPU time and memory requirement of the present method with an existing method has also been given.