From Petri Nets to differential equations: An integrative approach for biochemical network analysis

We report on the results of an investigation into the integration of Petri nets and ordinary differential equations (ODEs) for the modelling and analysis of biochemical networks, and the application of our approach to the model of the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway. We show that analysis based on a discrete Petri net model of the system can be used to derive the sets of initial concentrations required by the corresponding continuous ordinary differential equation model, and no other initial concentrations produce meaningful steady states. Altogether, this paper represents a tutorial in step-wise modelling and analysis of larger models as well as in structured design of ODEs

Batch Deterministic and Stochastic Petri Nets and Transformation Analysis Methods

International audienc

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

An introduction to Biomodel engineering, illustrated for signal transduction pathways

BioModel Engineering is the science of designing, constructing and analyzing computational models of biological systems. It is inspired by concepts from software engineering and computing science. This paper illustrates a major theme in BioModel Engineering, namely that identifying a quantitative model of a dynamic system means building the structure, finding an initial state, and parameter fitting. In our approach, the structure is obtained by piecewise construction of models from modular parts, the initial state is obtained by analysis of the structure and parameter fitting comprises determining the rate parameters of the kinetic equations. We illustrate this with an example in the area of intracellular signalling pathways

Simulation of a low voltage customer microgrid using petri nets

With renewable energy coming to the forefront of how power is generated and delivered to the modern consumer, Microgrids are emerging as an optimal and efficient method for implementing renewables and changing the infrastructure of the dated transmission and distribution grid. This thesis work presents mathematical models of Petri Nets for the simulation of a low voltage customer Microgrid. Using previous work created in this specific field, a Hybrid Petri Net is modified such that it consists of multiple distributed generators, storage, and the utility which is referred to as the main distribution grid in this thesis. A Discrete Petri Net is developed for load shedding which is critical for simulation purposes. Two types of Scheduling are developed, heuristic and reliability ones for the Microgrid to operate. Equations for firing rates are obtained for continuous transitions. Input weather data is obtained from outside sources and modified for the simulation. Computer programs are created for the microgrid simulation and the creation and presentation of the reachability graphs. A total of twelve simulations are run with the data analyzed and reachability graphs for the hybrid and discrete load shedding Petri nets developed for two simulations

Redes de Petri híbridas adaptativas : alcanzabilidad y ausencia de bloqueos

Las redes de Petri (RdP) son un paradigma formal ampliamente aceptado para el modelado de sistemas de eventos discretos. No obstante, con poblaciones de gran tamaño, aparece el problema de la explosión de estados (crecimiento exponencial del tamaño del conjunto de estados alcanzables). Una manera de paliar este problema consiste en fluidificar el formalismo y considerar redes de Petri continuas, que permiten abordar de manera eficiente el estudio de los sistemas mediante técnicas lineales de análisis. Sin embargo, las RdP continuas no siempre preservan sus propiedades, como por ejemplo la ausencia de bloqueos. En este Trabajo se introduce, formaliza y estudia un formalismo nuevo, denominado redes de Petri híbridas adaptativas (HAPN), que combina comportamiento continuo y discreto: El comportamiento de las transiciones de la red adaptativa es variable: una transición se comporta como continua si su carga de trabajo supera un umbral establecido inicialmente, en caso contrario se comporta como discreta. Estas redes pueden aproximar mejor las redes discretas, mientras que cuando las poblaciones son elevadas el comportamiento es continuo y las técnicas lineales son aplicables, evitando el problema de la explosión de estados. De esta manera, las HAPN constituyen un marco conceptual muy general que incluye a las redes de Petri discretas,continuas e híbridas. En este trabajo, se ha definido formalmente el formalismo de redes de Petri adaptativas. A continuación, se ha caracterizado el conjunto de marcados alcanzables de las redes de Petri adaptativas, así como se compara con el de las RdP discretas. Por ultimo, se ha estudiado la propiedad de ausencia de bloqueos: se trata de determinar si la red adaptativa preserva la ausencia de bloqueos de la red discreta con misma estructura y marcado inicial

Balancing static islands in dynamically scheduled circuits using continuous petri nets

High-level synthesis (HLS) tools automatically transform a high-level program, for example in C/C++, into a low-level hardware description. A key challenge in HLS is scheduling, i.e. determining the start time of all the operations in the untimed program. A major shortcoming of existing approaches to scheduling – whether they are static (start times determined at compile-time), dynamic (start times determined at run-time), or a hybrid of both – is that the static analysis cannot efficiently explore the run-time hardware behaviours. Existing approaches either assume the timing behaviour in extreme cases, which can cause sub-optimal performance or larger area, or use simulation-based approaches, which take a long time to explore enough program traces. In this article, we propose an efficient approach using probabilistic analysis for HLS tools to efficiently explore the timing behaviour of scheduled hardware. We capture the performance of the hardware using Timed Continous Petri nets with immediate transitions, allowing us to leverage efficient Petri net analysis tools for making HLS decisions. We demonstrate the utility of our approach by using it to automatically estimate the hardware throughput for balancing the throughput for statically scheduled components (also known as static islands) computing in a dynamically scheduled circuit. Over a set of benchmarks, we show that our approach on average incurs a 2% overhead in area-delay product compared to optimal designs by exhaustive search

Balancing Static Islands in Dynamically Scheduled Circuits using Continuous Petri Nets

High-level synthesis (HLS) tools automatically transform a high-level program, for example in C/C++, into a low-level hardware description. A key challenge in HLS is scheduling, i.e. determining the start time of all the operations in the untimed program. A major shortcoming of existing approaches to scheduling – whether they are static (start times determined at compile-time), dynamic (start times determined at run-time), or a hybrid of both – is that the static analysis cannot efficiently explore the run-time hardware behaviours. Existing approaches either assume the timing behaviour in extreme cases, which can cause sub-optimal performance or larger area, or use simulation-based approaches, which take a long time to explore enough program traces. In this article, we propose an efficient approach using probabilistic analysis for HLS tools to efficiently explore the timing behaviour of scheduled hardware. We capture the performance of the hardware using Timed Continous Petri nets with immediate transitions, allowing us to leverage efficient Petri net analysis tools for making HLS decisions. We demonstrate the utility of our approach by using it to automatically estimate the hardware throughput for balancing the throughput for statically scheduled components (also known as static islands) computing in a dynamically scheduled circuit. Over a set of benchmarks, we show that our approach on average incurs a 2% overhead in area-delay product compared to optimal designs by exhaustive search

Hybrid Petri net model of a traffic intersection in an urban network

Control in urban traffic networks constitutes an important and challenging research topic nowadays. In the literature, a lot of work can be found devoted to improving the performance of the traffic flow in such systems, by means of controlling the red-to-green switching times of traffic signals. Different techniques have been proposed and commercially implemented, ranging from heuristic methods to model-based optimization. However, given the complexity of the dynamics and the scale of urban traffic networks, there is still a lot of scope for improvement. In this work, a new hybrid model for the traffic behavior at an intersection is introduced. It captures important aspects of the flow dynamics in urban networks. It is shown how this model can be used in order to obtain control strategies that improve the flow of traffic at intersections, leading to the future possibility of controlling several connected intersections in a distributed way