This paper presents an approach to using Stochastic Petri nets to model large-scale concurrent systems, in our case, a scalable computer interconnect. We show how Stochastic Petri net models can exploit the symmetry of the system to construct a tractable, but approximate, analytic model, and that they can yield results very close to those of a detailed simulation model, with much less computati...

This paper presents new methods for the transient and stationary analysis of stochastic Petri nets with exponentially distributed and deterministic ring delays. The method of supplementary variables is used for the derivation of general state equations which describe the temporal behavior of the underlying stochas-tic process. Numerical algorithms are presented for the solution of the state equ...

In this paper we investigate the effect of three time-triggered system rejuvenation policies on service availability using a queuing model. The model is formulated as an extended stochastic Petri net using a variety of distributions for times between state changes. We define a metric for steady-state service availability and derive how it can be estimated from the models. We further analyze tim...

This paper presents an extension of the Generalized Stochastic Petri Net (GSPN) formalism that enables the computation of first passage time distributions. The tagged customer technique typical of queuing networks is adapted to the GSPN context by providing a formal definition and an automatic computation of the groups of tokens that can be identified as customers, i.e. classes of homogeneous e...

Petri nets are frequently used for modeling and analysis of discrete event systems. Similar to other modeling formalisms for discrete systems, it suffers from state explosion. Fluidification can be used to overcome this difficulty yielding fluid approximation of original Petri nets in the sense of behaviours and properties. This models are called continuous Petri nets. In this work, stochastic ...

We present results of a collaboration project, during which parts of General Motors’ north American vehicle supply chain have been modeled and evaluated. A variant of colored stochastic Petri nets has been developed for this task, and support for model creation and performance evaluation was implemented in our tool TimeNET. Variations of the model and their stepwise evaluation lead to suggestio...

This paper proposes a simplification of the stochastic Petri nets graphical notation with the purpose of defining a more compact and clearer graphical way of building formal models of biological phenomena. Three biological examples are first presented, then modeled with the classical SPN modeling formalism, and their key modeling patterns distilled to identify the main features that need to be ...

An extension of regular nets, a class of coloredd nets, to a stochastic model is proposed. We show that the symmetries in this class of nets make it pos sible to developp a performance evaluation by constructingg only a graph of symbolic markings, which ver tices are classes of states, insteadd of the whole reachability graph. Usingg algebraic techniques, we prove that all the states in a class...

Several different models for predicting coverage in a fault-tolerant system are discussed, including models for permanent, intermittent, and transient errors. Markov, semi-Markov, nonhomogeneous Markov, and extended stochastic Petri net models for computing coverage are developed. Two types of events which interfere with recovery are examined; methods for modeling such events (applicable if the...

Product-form models facilitate the efficient analysis of large stochastic models and have been sought after for some three decades. Apart from the dominating work on queueing networks, some product-forms were found for stochastic Petri nets (SPNs) that allow forkjoin constructs and for queueing networks extended to include special customers called signals, viz. G-networks. We appeal to the Reve...