We describe an investigation into spatial modelling by means of an ongoing case study, namely phase variation patterning in bacterial colony growth, forming circular colonies on a flat medium. We explore the application of two different geometries, rectangular and circular, for modelling and analysing the colony growth in 2.5 dimensions. Our modelling paradigm is that of coloured stochastic Pet...

In this study we extend stochastic-calculus allowing general probabilistic distributions to occur in its preexes. We show that no additional information is needed in the labels of transitions or in the states of systems to derive an enabling relation between transitions. Enabling is then used to compute the residual life times of parallel activities that are not immediately selected when enable...

Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in recent years to increase their modeling power, or their capability to handle large systems. This...

Whether a real system is approximated in a discrete or continuous simulation model depends on the more predominating type of variables determining the system’s behavior over time. If both discretely and continuously changing variables have to be considered, hybrid simulation techniques have to be applied, where discrete events have an influence on the otherwise continuously changing system stat...

We consider finite-population and finite-capacity polling systems. The behavior of these systems is described by means of generalized stochastic Petri nets. The exact results for the mean response times are obtained numerically by means of the stochastic Petri net package. Finite population polling systems are generally difficult to analyze. Thus, one of the contributions of this paper is the f...

This paper presents an analytical approach for the analysis of non-Markovian stochastic Petri nets. The primary aim of the presented solution method is its universal applicability. Therefore, an approach based on discrete phase type distributions has been chosen to perform the necessary Markovization. For the handling of the resulting state space explosion problem, symbolic storage structures, ...

Petri nets in which random firing delays are associated with transitions whose firing is a n atomic opemtion are known under the name "stochastic Petri nets". These models are discussed, with the purpose of ezplaining why they were proposed in the performance evaluation field, why random delays with negative ezponential probability density functions are mainly used, and what are their strong an...

CSL is a stochastic temporal logic that has been defined for continuous time Markov chains, and that allows the checking of whether a single state, or a set of states, satisfies a given probabilistic condition defined over states or over a path of states. In this paper we consider the problem of CSL model checking in the context of Generalized Stochastic Petri Nets. We present a translation fro...

The failure and repair of modules in an N-Modular Redundant (NMR) system are governed by a failure time distribution and repair time distribution, respectively. It is generally reasonable to assume that a module’s failure time distribution is a simple exponential distribution. However, it is not reasonable to assume that the repair time distribution is also exponential. Reliability models with ...