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...

We study the introduction of transitions with Phase-type distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works...

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...

The future European Train Control System (ETCS) will be based on mobile communication and overcome fixed blocks in order to increase track utilization and interoperability throughout Europe. Data processing on board the train and in radio block centers as well as the radio communication link are crucial factors for the safe and efficient operation. Their real-time behavior under inevitable link...

The product form results recently published for Stochastic Petri Nets are combined with the well known product form results for Queueing Networks in the model formalism of Queueing Petri Nets yielding the class of product form Queueing Petri Nets. This model class includes Stochastic Petri Nets with product form solution and BCMP Queueing Networks as special cases. We introduce an arrival theor...

Motivated by the need for performance models suitable for modeling and evaluation of wireless sensor networks, we introduce a retrial queueing system with a finite number of homogeneous sources, unreliable servers, orbital search, and unreliable orbit. All random variables involved in model construction are assumed to be independent and exponentially distributed. Providing a generalized stochas...

Many distributed systems are still too large to be handled. Thus, it’s important to find techniques that can be used to extend the size of the systems that can be verified and analyzed. In this paper, we study the qualitative and quantitative performance of the distributed systems that can be interacting with each other by using Temporized Stochastic Petri Net (TSPN) [5]. We consider then the c...

The solution of a generalized stochastic Petri net (GSPN) is severely restricted by the size of its underlying continuous-time Markov chain. In recent work, matrix diagrams built from a Kronecker expression for the transition rate matrix of certain types of GSPNs were shown to allow for more efficient solution; however, the GSPN model requires a special form, so that the transition rate matrix ...