Gianfranco Balbo

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

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.

Modelling with Generalized Stochastic Petri Nets

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.

The effect of execution policies on the semantics and analysis of stochastic Petri nets

Petri nets in which random delays are associated with atomic transitions are defined in a comprehensive framework that contains most of the models already proposed in the literature. To include generally distributed firing times into the model one must specify the way in which the next transition to fire is chosen, and how the model keeps track of its past history; this set of specifications is called an execution policy. A discussion is presented of the impact that different execution policies have on semantics of the mode, as well as the characteristics of the stochastic process associated with each of these policies. When the execution policy is completely specified by the transition with the minimum delay (race policy) and the firing distributions are of the phase type, an algorithm is provided that automatically converts the stochastic process into a continuous time homogeneous Markov chain. An execution policy based on the choice of the next transition to fire independently of the associated delay (preselection policy) is introduced, and its semantics is discussed together with possible implementation strategies. >

Generalized stochastic Petri nets: a definition at the net level and its implications

The class of Petri nets obtained by eliminating timing from generalized stochastic Petri net (GSPN) models while preserving the qualitative behavior is identified. Structural results for those nets are derived, obtaining the first structural analysis of Petri nets with priority and inhibitor arcs. A revision of the GSPN definition based on the structural properties of the models is presented. It is shown that for a (wide) class of nets, the definition of firing probabilities of conflicting immediate transitions does not require the information on reachable markings. Identification of the class of models for which the net-level specification is possible is also based on the structural analysis results. The procedure for the model specification is illustrated by means of an example. It is also shown that a net-level specification of the model associated with efficient structural analysis techniques can have a substantial impact on model analysis. >

Introducation to stochastic Petri nets

Stochastic Petri Nets are a modelling formalism that can be conveniently used for the analysis of complex models of Discrete Event Dynami Systems (DEDS) and for their performance and reliability evaluation. The automatic construction of the probabilistic models that underly the dynamic behaviours of these nets rely on a set of results that derive from the theory of untimed Petri nets. The paper introduces the basic motivations for modelling DEDS and briefly overviews the basic results of net theory that are useful for the definition of Stochastic Petri Nets and Generalized Stochastic Petri Nets. The different approaches that have been used for introducing the concept of time in these models are discussed in order to provide the basis for the definition of SPNs and GSPNs as well. Details on the solution techniques and on their computational aspects are provided. A brief overview of more advanced material is included at the end of the paper to highlight the state of the art in this field and to give pointers to relevant results published in the literature.

Combining queueing networks and generalized stochastic Petri nets for the solution of complex models of system behavior

A technique is presented whereby queueing network models and generalized stochastic Petri nets are combined in such a way as to exploit the best features of both modeling techniques. The resulting hierarchical modeling approach is useful in the solution of complex models of system behavior. The authors have chosen two examples from the recent literature to illustrate the power and scope of this technique. They also demonstrate how folding of the generalized stochastic Petri net models for these two examples is useful in obtaining efficiently solvable, approximate models (bounding models). >

An introduction to generalized stochastic Petri nets

Abstract The paper decribes the GSPN approach to the performance evaluation of distributed systems. The structural properties and temporal specifications of GSPN are summarized, and application examples are then illustrated, trying to emphasize the methodology to be followed in the model development and validation, rather than the numerical results that can be obtained from the specific models developed in the paper.

Asymptotic analysis of multiclass closed queueing networks: multiple bottlenecks

Abstract Asymptotic expressions for the values of throughputs, utilizations, mean queue lengths, and mean cycle times are derived for multiclass product-form queueing networks with load independent servers, where different (sets of) stations may behave as bottlenecks when different population mixes load the network. The space of possible population mixes is shown to be partitioned into sectors within which several stations may saturate together. Analytic expressions for the computation of the edges of these sectors are provided. A synthesis of a large set of experiments is presented to numerically support a conjecture that is used to perform the asymptotic analysis of this class of networks.

Introduction to generalized stochastic Petri nets

Generalized Stochastic Petri Nets are a modelling formalism that can be conveniently used for the analysis of complex models of Discrete Event Dynamic Systems and for their performance and reliability evaluation. The automatic construction of the probabilistic models that underly the dynamic behaviours of these nets rely on a set of results that derive from the theory of untimed Petri nets. The paper briefly surveys some results of net theory together with the different approaches used to introduce the concept of time in these models that are useful for the definition of Stochastic Petri Nets and Generalized Stochastic Petri Nets. Details on the solution techniques and on their computational aspects are provided. A brief overview of advanced material is included at the end of the paper to highlight the state of the art in this field and to give pointers to relevant results published in the literature.

A class of generalised stochastic petri nets for the performance evaluation of multiprocessor systems

Graph models have been proposed by many authors as a useful tool for the analysis of peculiar features of computer systems such as concurrency, synchronization, communication, and cooperation among subsystems. Much of the work in this field is related to the original ideas developed by C. A. Petri. These graph models are today generally known as Petri Nets (PNs).