Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

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Petri nets: Properties, analysis and applications

Generalized stochastic Petri nets (GSPNs) are presented and are applied to the performance evaluation of multiprocessor systems. GSPNs are derived from standard Petri nets by partitioning the set of transitions into two subsets comprising timed and immediate transitions. An exponentially distributed random firing time is associated with each timed transition, whereas immediate transitions fire in zero time. It is shown that GSPN are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented. Examples of application of gspn models to the performance evaluation of multiprocessor systems show the usefulness and the effectiveness of this modeling tool. 15 references.

A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems

A model of commumcations protocols based on finite-state machines is investigated. The problem addressed is how to ensure certain generally desirable properties, which make protocols \"wellformed,\" that is, specify a response to those and only those events that can actually occur. It is determined to what extent the problem is solvable, and one approach to solving it ts described. Categories and SubJect Descriptors' C 2 2 [Computer-Conununication Networks]: Network Protocols-protocol verification; F 1 1 [Computation by Abstract Devices] Models of Computation--automata; G.2.2 [Discrete Mathematics] Graph Theory--graph algoruhms; trees General Terms: Reliability, Verification Additional

On Communicating Finite-State Machines

A description and analysis of concurrent systems, such as communication systems, whose behavior is dependent on explicit values of time is presented. An enumerative method is proposed in order to exhaustively validate the behavior of P. Merlin's time Petri net model, (1974). This method allows formal verification of time-dependent systems. It is applied to the specification and verification of the alternating bit protocol as a simple illustrative example. >

Modeling and verification of time dependent systems using time Petri nets

An isomorphism between the behavior of Petri nets with exponentially distributed transition rates and Markov processes is presented. In particular, k-bounded Petri nets are isomorphic to finite Markov processes and can be solved by standard techniques if k is not too large. As a practical example, we solve for the steady state average message delay and throughput on a communication link when the alternating bit protocol is used for error recovery.

Performance Analysis Using Stochastic Petri Nets

A study is presented which permits the formal analysis and synthesis of recoverable computer communication protocols. This study is based on a formal representation of processes by a model of computation, the Petri nets (PN's). The PN model is generalized to include a representation of the possible failures, and then, the concept of "recoverability" is formally defined. A set of necessary and sufficient conditions which a process must satisfy in order to be recoverable is derived. In the PN model, the processes that satisfy these conditions are shown to have some practical limitations. A new model, the time-Petri net (TPN), is introduced to remove these limitations. This new model allows the introduction of constraints in the execution times of its part. As shown in this paper, the TPN appears to be a suitable model for the study of practical recoverable processes. Several practical communication protocols are formally designed and analyzed using this new model, and some interesting properties of these protocols are formally derived.

Recoverability of Communication Protocols--Implications of a Theoretical Study

This paper presents a coherent method which permits the specification, check out, and implementation of communication protocols. Although this work is mainly directed towards telephone signaling in a programmable environment, the philosophy and most of the tools can be effectively used to handle the most general situations in which two entities interact by any kind of protocol. Since the proposed approach reduces the possibility of errors and inconsistencies, minimizes the programming needed, and improves the documentation and understandability, we believe that this methodology will facilitate the installation or modification of complex trunk protocols and other communication protocols.

P. Merlin

Papers

Recoverability of Communication Protocols--Implications of a Theoretical Study

A Methodology for the Design and Implementation of Communication Protocols