Cluster Grid based Response-time analysis module for the PIPE Tool.

Generalized Stochastic Petri Nets (GSPNs) are a widely used high-level formalism used for modelling discrete-event systems. The Platform Independent Petri net Editor (PIPE) is an open source software project that allows creation, analysis and simulation of Petri Nets. This tool paper presents a PIPE module for response-time analysis of a Petri net’s underlying Continuous Time Markov Chain (CTMC). Jobs are submitted via a web interface, from within PIPE or from a browser. The parallel computations are run using Grid Engine on a cluster hosted at Imperial College London. 1

Stochastic simulation efficiency

The work described in this report can be broadly divided into two sections. The first section considers two export features. We describe how the export for stochastic Petri nets to SBML level 1 has been added to the Petri net modelling and simulation tool Snoopy. This task was accomplished by making appropriate changes to the existing export code to generate SBML level 2. Also we demonstrate in detail, how the direct export for coloured Petri nets to both levels (i.e. 1 and 2) of SBML was realised. The next section summarises the performed comparison of different stochastic simulation tools for biochemical reaction networks. We first compare BioNetGen and SSC with each other by performing simulations on non-coloured Petri nets. Then, we compare the remaining four tools, i.e. Cain, Marcie, Snoopy and Stochkit with each other by performing simulation on coloured Petri nets. This work builds on results by Aman Sinha [19]

Deriving the performance indices in product-form stochastic Petri nets: Open problems and simulation

Stochastic Petri nets are an important formalism used for the performance evaluation of computer and communication systems as well as other fields like bioin-formatics and logistics. Despite its high flexibility and modelling power, one of the problems of quantitative analyses based on stochastic Petri nets is the state space explosion, i.e., the high cardinality reached by the state space of even a structurally small SPN. As a consequence a direct analysis of the Markovian processes underlying the models is not feasible. Product-form Petri nets are a class of stochastic Petri nets whose invariant measure can be expressed as a product of functions, each of which depends only on a marking of a single place. Nevertheless, for the effective computation of the performance indices the computation of the stationary distribution is required. In this paper we propose a classification of product-form stochastic Petri nets based on the availability of algorithms for the computation of their stationary performance indices. Moreover, in case simulation is required, we introduce two stopping criteria that exploit the product-form property of the nets

Compositional modelling using Petri nets with the analysis power of stochastic hybrid processes

A general stochastic hybrid process (GSHP) is a mathematical formalism that covers most of the requirements posed by the modelling of complex operations, such as time dependencies, multi-dimensional continuous as well as discrete processes, discontinuities, randomness and model uncertainties. In addition, it is possible to study GSHP by using stochastic analysis methodologies, thereby empowering it with powerful mathematical properties. This guarantees unambiguous simulation possibility of the model and allows speeding up this simulation while keeping the model properties intact. However, using GSHP to construct a model of a complex operation is not easy. To support the modelling and the subsequent verification both by mathematical and by multiple operational domain experts, a supporting graphical modelling formalism is desired. Petri nets have shown to be useful for developing models of various complex applications. Typical Petri net features are concurrency and synchronisation mechanism, hierarchical and modular construction, and natural expression of causal dependencies, in combination with graphical and analytical representations.\ud \ud The aim of this thesis is to combine the strengths of Petri net modelling formalisms and those of GSHP. First, dynamically coloured Petri nets (DCPN) are developed, and proof of equivalence is provided with piecewise deterministic Markov processes, which is a particular class of GSHP. Next, DCPN are extended to stochastically and dynamically coloured Petri nets (SDCPN), and proof of equivalence is provided with GSHP. Subsequently, SDCPN are extended to SDCPN with interconnection mapping types (SDCPNimt) and proof of equivalence is provided with both SDCPN and GSHP. It is shown with illustrative air transport examples that these three classes of Petri net are very effective when it comes to the compositional modelling of operations consisting of many distributed components that behave and interact in a dynamic way with many uncertainties. With the equivalence relations between these formalisms, the properties and strengths of the various approaches are combined. The many applications of the approach developed in this thesis, executed at NLR and beyond, show that both the approach and its combined strengths are acknowledged and supported by practice

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Analysis of signalling pathways using the prism model checker

We describe a new modelling and analysis approach for signal transduction networks in the presence of incomplete data. We illustrate the approach with an example, the RKIP inhibited ERK pathway [1]. Our models are based on high level descriptions of continuous time Markov chains: reactions are modelled as synchronous processes and concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis of queries such as if a concentration reaches a certain level, will it remain at that level thereafter? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

A case study in model-driven synthetic biology

We report on a case study in synthetic biology, demonstrating the modeldriven design of a self-powering electrochemical biosensor. An essential result of the design process is a general template of a biosensor, which can be instantiated to be adapted to specific pollutants. This template represents a gene expression network extended by metabolic activity. We illustrate the model-based analysis of this template using qualitative, stochastic and continuous Petri nets and related analysis techniques, contributing to a reliable and robust design

Internet enabled modelling of extended manufacturing enterprises using the process based techniques

The paper presents the preliminary results of an ongoing research project on Internet enabled process-based modelling of extended manufacturing enterprises. It is proposed to apply the Open System Architecture for CIM (CIMOSA) modelling framework alongside with object-oriented Petri Net models of enterprise processes and object-oriented techniques for extended enterprises modelling. The main features of the proposed approach are described and some components discussed. Elementary examples of object-oriented Petri Net implementation and real-time visualisation are presented

Flux Analysis in Process Models via Causality

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly recognised model of concurrency, and state transitions of process models, seen as Petri nets. We show that we can this way extract the causal resource dependencies in simulations between individual state transitions as partial orders of events. We propose transformations on the partial orders that provide means for further analysis, and introduce a software tool, which implements these ideas. By means of an example of a published model of the Rho GTP-binding proteins, we argue that this approach can provide the substitute for flux analysis techniques on ordinary differential equation models within the stochastic setting of process algebras

Computational Modeling for the Activation Cycle of G-proteins by G-protein-coupled Receptors

In this paper, we survey five different computational modeling methods. For comparison, we use the activation cycle of G-proteins that regulate cellular signaling events downstream of G-protein-coupled receptors (GPCRs) as a driving example. Starting from an existing Ordinary Differential Equations (ODEs) model, we implement the G-protein cycle in the stochastic Pi-calculus using SPiM, as Petri-nets using Cell Illustrator, in the Kappa Language using Cellucidate, and in Bio-PEPA using the Bio-PEPA eclipse plug in. We also provide a high-level notation to abstract away from communication primitives that may be unfamiliar to the average biologist, and we show how to translate high-level programs into stochastic Pi-calculus processes and chemical reactions.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005