Modelling and controlling traffic behaviour with continuous Petri nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a compositional formalism to model traffic behaviour. This paper introduces some new features of continuous Petri nets that are useful to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing trac light controllers that minimize the total delay of the vehicles in the system

Hybrid modeling and optimization of biological processes

Proß S. Hybrid modeling and optimization of biological processes. Bielefeld: Bielefeld University; 2013

Flexible Nets: a modeling formalism for dynamic systems with uncertain parameters

Funder: FP7 People: Marie-Curie Actions; doi: https://doi.org/10.13039/100011264; Grant(s): 623995Abstract: The modeling of dynamic systems is frequently hampered by a limited knowledge of the system to be modeled and by the difficulty of acquiring accurate data. This often results in a number of uncertain system parameters that are hard to incorporate into a mathematical model. Thus, there is a need for modeling formalisms that can accommodate all available data, even if uncertain, in order to employ them and build useful models. This paper shows how the Flexible Nets (FNs) formalism can be exploited to handle uncertain parameters while offering attractive analysis possibilities. FNs are composed of two nets, an event net and an intensity net, that model the relation between the state and the processes of the system. While the event net captures how the state of the system is updated by the processes in the system, the intensity net models how the speed of such processes is determined by the state of the system. Uncertain parameters are accounted for by sets of inequalities associated with both the event net and the intensity net. FNs are not only demonstrated to be a valuable formalism to cope with system uncertainties, but also to be capable of modeling different system features, such as resource allocation and control actions, in a facile manner

BioSimulator.jl: Stochastic simulation in Julia

Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, BioSimulator.jl, for implementing the Gillespie algorithm, $\tau$-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools. We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time. BioSimulator.jl's interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics. The user-friendly nature of BioSimulator.jl encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification.Comment: 27 pages, 5 figures, 3 table

Petri net models of microgrids with distributed generators

This thesis introduces some basic concepts and control methods about a microgrid. Then, two hot issues are investigated. One is how to control multiple distributed generators; and another is how to model both discrete event and continuous behaviors of a microgrid. To address these two issues, this thesis work applies Petri nets to both modeling and control of a microgrid. Ordinary Petri nets, hybrid Petri nets, and finite capacity Petri nets, are introduced with their examples targeted at modeling the behavior of a microgrid. Coordination control of multiple distributed generators based on a Petri net model is proposed. Compared with multi-V/f control, the Petri net based control enables the system to operate with a longer stable time interval. Finally, a hybrid Petri net model is constructed to model both discrete event and continuous behaviors of an on-load tap changing transformer system. Compared with an algebraic method, the hybrid Petri net offers a clear and easy-to-understand method to describe such a system

Measurements, Models, Systems and Design

531 s.

Modeling, analyzing and controlling hybrid systems by Guarded Flexible Nets

A number of artificial and natural systems can be modeled as hybrid models in which continuous and discrete variables interact. Such hybrid models are usually challenging to analyze and control due to the computational complexity associated with existing methods. In this paper, the novel modeling formalism of Guarded Flexible Nets (GFNs) is proposed for the modeling, analysis and control of hybrid system. A GFN consists of an event net that determines how the state changes as processes execute, and an intensity net that determines the speeds of the processes. In a GFN, the continuous state is given by the value of its state variables, and the discrete state is given by the region within which such variables lie. GFNs are shown to possess a high modeling power while offering appealing analysis and control possibilities