The traac equations are a set of linear equations, which are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traac equations are therefore of great importance. This note provides a necessary and suucien...

Failure diagnosis in large and complex systems is a critical task. A discrete event system (DES) approach to the problem of failure diagnosis is presented in this paper. A classic solution to solve DES’s diagnosis is a stochastic Petri net. The foraging behavior of ant colonies can give rise to the shortest path, which will reduce the state explosion of stochastic Petri net. Therefore, a new mo...

This paper discusses the analysis of stochastic Petri nets using the proxelbased simulation method. The paradigm of the proxel (”probability element”) was recently introduced in order to provide a new algorithmic approach to analysing discrete-state stochastic models such as are represented by stochastic Petri nets (SPNs) or queuing systems. Proxel-based simulation is not related to either of t...

Realistic models of computer and communication systems result in large, complex performance models. Compositionality, offered by stochastic process algebra constructs a model from submodels which are smaller and more tractable. We present a technique to exploit this structure in order to enhance the solution of the model by decomposition of the underlying Markov process. The decomposition under...

Some insight on the meaning of “modeling power” for Stochastic Petri Net models is given. Extensions characterizing a Stochastic Petri Net are categorized as logical or stochastic. Three logical constructs are shown to be equivalent: inhibitor arcs, transition priorities, and enabling functions associated with the transitions. A direct transformation of Petri Nets with inhibitor arcs into Petri...

This paper presents a new net-reduction methodology to facilitate the analysis of large workflow models. We propose an enhanced algorithm based on reducible subnet identification which preserves both soundness and completion time distribution. Moreover we outline an approach to model the dynamic behavior of business processes by exploiting the power of a class of non-Markovian stochastic Petri ...

In this paper we characterize a class of stochastic Petri nets that can be solved using matrix geometric techniques. Advantages of such an approach are that very eecient mathematical technique become available for practical usage, as well as that the problem of large state spaces can be circumvented. We rst characterize the class of stochastic Petri nets of interest by formally deening a number...

Process mining is a tool to extract non-trivial and useful information from process execution logs. These so-called event logs (also called audit trails, or transaction logs) are the starting point for various discovery and analysis techniques that help to gain insight into certain characteristics of the process. In this paper we use a combination of process mining techniques to discover multip...

System analysis is often needed with respect to both qualitative and quantitative aspects. In the last decades, several formalisms have been developed that attempt to combine these aspects in one description. Present emphasis is on Stochastic Petri Nets. Amongst others, one disadvantage of these formalisms lies with the diiculties when describing scheduling strategies with Petri Net elements. T...

A Markovian Petri net is a stochastic discrete event system frequently used for analysis and performance evaluation purposes. In the past, the fluidification has been proposed as a relaxation technique for avoiding the ”state explosion problem”. Following the same approach, in this paper a hybrid Petri net model is defined as a partial relaxation of an original Markovian Petri net. It is shown ...