From the Publisher:
This book presents a unified theory of Generalized Stochastic Petri Nets (GSPNs) together with a set of illustrative examples from different application fields. The continuing success of GSPNs and the increasing interest in using them as a modelling paradigm for the quantitative analysis of distributed systems suggested the preparation of this volume with the intent of providing newcomers to the field with a useful tool for their first approach. Readers will find a clear and informal explanation of the concepts followed by formal definitions when necessary or helpful. The largest section of the book however is devoted to showing how this methodology can be applied in a range of domains.

Modelling with Generalized Stochastic Petri Nets

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

1. Introduction 2. Background 3. Performance evaluation process algebra 4. Modelling study: multi-server multi-queue systems 5. Notions of equivalence 6. Isomorphism and weak isomorphism 7. Strong bisimilarity 8. Strong equivalence 9. Conclusions Bibliography Index.

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A Compositional Approach to Performance Modelling

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 class of Petri nets (DSPN) in which transitions can fire after either a deterministic or a random, exponentially distributed, firing delay is defined, and a solution technique is presented to obtain the steady-state probability distribution over markings, introducing restrictions on the use of deterministic firing delays. An example of application of this modeling technique is presented to demonstrate the impact that the use of a mix of deterministic and exponentially distributed firing delays (instead of all exponentially distributed firing delays) can have on performance and reliability estimates.

Michael Karl Molloy

Papers

On the integration of delay and throughput measures in distributed processing models