System level understanding of the repetitive cycle of cell growth and division is crucial for disclosing many unexpected principles of biological organisms. The deterministic or stochastic approach are alone not sufficient to study such cell regulation due to the complex reaction network and the existence of reactions with different time scales. Thus, integration of both approaches is necessary...

Traditional mathematical models are focussed on the construction of kinetic models by solving algebraic equations for steady states and systems of differential equations for time-dependent states (for a review see Heinrich & Schuster [4]). Petri net theory exhibits a mathematical formalism to model, analyze, and simulate discrete event systems with inherent concurrency (Peterson [7], Starke [9]...

We compare discrete-state stochastic Petri nets (SPNs) and fluid stochastic Petri nets (FSPNs) with a mixed discrete-continuous state space in their application to openloop video broadcasting systems. For both classes, we present models of the Video-on-Demand client-server system, which generally capture all relevant system aspects in a concise and graphical way. Differences in model design as ...

Performance/dependability evaluation via modeling results in fast and economic system development. Traditionally, simulations have been used to evaluate realistic systems but do not yield exact results. Analytic solution methods can yield exact results, but can su er from the state-space explosion problem. A reduced base model construction technique for stochastic activity networks, which explo...

Computer-aided modeling has become an accepted technique for predicting the performance and dependability of computer-communication networks. Many model formalisms have been proposed for this purpose, and have achieved varying degrees of success. One particular model type, stochastic Petri nets, has received considerable attention during the last ten years. Several classes of models of this typ...

The advantages of the compositional structure within the Markovian process algebra PEPA for model construction and simplification have already been demonstrated. In this paper we show that for some PEPA models this structure may also be used to advantage during the solution of the model. Several papers offering product form solutions of stochastic Petri nets have been published during the last ...

19 to both control the uid ow, and have the discrete control decisions be aaected by observed uid ow. We have provided formal deenition of FSPNs and developed the rules for their dynamic evolution. We have derived coupled systems of partial diierential equations for the transient and the steady-state behavior of FSPNs. Spectral representation of the FSPNs with a single continuous place can be a...

Stochastic Petri nets (SPNs) is a well-known model for quantitative analysis. We consider the class called DTWSPNs that is a modification of discrete time SPNs (DTSPNs) by transition labeling and weights. Transitions of DTWSPNs are labeled by actions that represent elementary activities and can be visible or invisible for an external observer. For DTWSPNs, interleaving and step probabilistic τ ...

Shortest path problem in stochastic graphs has been recently studied in the literature and a number of algorithms has been provided to find it using varieties of learning automata models. However, all these algorithms suffer from two common drawbacks: low speed and lack of a clear termination condition. In this paper, we propose a novel learning automata-based algorithm for this problem which c...