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

Dynamically Coloured Petri Nets for Air Traffic Management Safety Purposes

We present a model for the development of enzyme molecules under the action of its inhibitor. In this model the inhibitor’s population size is regulated by a piece-wise deterministic Markov process. This special class of stochastic processes is usually represented by a uniquely solvable system of ordinary differential equations (ODEs) perturbed by a discrete stochastic switching process. The assumption that enzyme molecules growth rate cannot be negative leads us to the alternative version of the model, where the right hand sides of the ODEs are only piece-wise differentiable. For this reason a standard procedure based on the analogue of the Malliavin calculus approach [17] is not enough to deal with the long-time behaviour of the trajectories of the process. However, in both cases, a proper Markov semigroup of the densities of the process is constructed. Moreover, its asymptotic stability in the sense of Lasota is shown in this paper.

Several approaches have been introduced to derive performance indices of software architectures automatically. Most of them apply the theory of queuing network models or Petri nets. We identify Unified Modeling Language (UML) state charts as a starting point for evaluation, and apply annotations and extensions on them before transforming them into a mathematical model. The mathematical formalism behind our investigations is based on discrete time quasi birth-death processes

Event-related control is considered in which process and related process control can be described by states and transitions that can be represented concisely by a Petri net (PN). Both process and related process control systems are event-related, causal, and concurrent and define a special type of PN using a few primitives that are assembled to form a net for which structural and dynamic invariants apply. The PNs can be used for a general approach to event-related process control in simulating, checking, debugging, and stating the quantitative deviations from the ideal solution for any given process control system. The technique can be applied to continuous or discrete processes, and provides formal checks at all development stages. It allows for components with nonideal behavior and yields numerical performance criteria. The invariants allow the PN to be structured in such a way that even complex process control systems become manageable. Examples are presented for the control tasks in an electrical substation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

International audience

Model checking Petri nets with MSVL

The optimization criterion is that reference point of the controlled systems, which provides the maximum coherence of the operational process results with the purpose of its owner. Difficulties of solving the tasks, connected with the choice of an adequate optimization criterion are caused by the fact that a large number of indicators intended for use as an optimization criterion have been developed and continue to be developed now. The verification process of the indicator, which can potentially be used as an optimization criterion, is rather difficult. This difficulty is caused by the fact that the identification process is based on an exclusion method. Those indicators that have shown contradictory results on the classes of operations models identified by the rating efficiency should be excluded from the “contenders”. During the researches, the hypothesis on the possibility of creating the reference models, allowing the development of direct verification methods wasn’t confirmed. However, the comparative research of cybernetic models of operations with different duration for consistency has allowed setting a restriction on the formation rules of models of this class and defining the rules of their equivalent converting. Besides, during the researches, the method of creating a class of simple operation models with the predetermined identification, concerning their rating efficiency, has been developed. This means that the rating creation of these models doesn't require determination of local efficiency criteria. Creation of a new class of reference models expands the possibilities of the estimated indicator verification method. At the same time, the positive effect of expansion of the opportunities of the verification method is shown not so much in an increase in the probability of excluding the inadequate estimated indicator, but in the introduction of a restriction on the rules of creating the classes of reference operation models. Introduction of a restriction prevents the possibility of excluding the adequate estimated indicator from consideration.

Switched stochastic systems (SSS) can be used to describe hybrid systems with randomness. However, the languages to describe their discrete switching logic and stochastic dynamic processes are different, and this difference makes their design and analysis hard. This paper proposes a new Petri net model, namely stochastic-differential Petri net (S-DPN), to describe both discrete switching logic, represented by a Markov chain, and stochastic dynamic processes, represented by a set of stochastic differential equations. We then apply a model checking technique to S-DPN to check the correctness of the requirements of SSS. A temperature control system is used to demonstrate the effectiveness of our method.

A piecewise deterministic Markov process (PDP) is a continuous time Markov process consisting of continuous, deterministic trajectories interrupted by random jumps. The trajectories may be controlled with the object of minimizing the expected costs associated with the process. A method of representing this controlled PDP as a discrete time decision process is presented, allowing the value function for the problem to be expressed as the fixed point of a dynamic programming operator. Decisions take the form of trajectory segments. The expected costs may then be minimized through a dynamic programming algorithm, rather than through the solution of the Bellman--Hamilton--Jacobi equation, assuming the trajectory segments are numerically tractable. The technique is applied to the optimal capacity expansion problem, that is, the problem of planning the construction of new production facilities to meet rising demand.

Based on the workflow management coalition (WFMC) standard and component software technologies, this paper addresses our Petri-nets-based approach for workflow and process automation. Petri nets provide graphical and mathematical formalisms for work-flow process definition and analysis. In this paper, we will present how to use Petri nets and a toolkit NCUPN (National Central University Petri Nets toolkit) for process definition and analysis. NCUPN is a Petri nets modeling and analysis toolkit developed to help software engineers in drawing and doing analysis. Once a workflow process is drawn using NCUPN, analysis can be done automatically. In this paper, we will demonstrate how to use NCUPN to analyze behavioral properties of workflow process, such as deadlock, liveness, safety, and starvation.

This paper proposes a Petri Net based methodology for task scheduling on multiproces sor architectures. The aim is to build automati cally a stochastic model (markovian model or stochastic simulation model) for both perfor mance evaluation and task scheduling. The modelling process that we use consists in the consecutive elaboration of two models: the knowledge model and the action model. The knowledge model is a formalization of the structure and the working of the system, using Petri Nets. This knowledge model is made of three parts: a logical subsystem (precedence constraints between tasks), a physical subsystem (multiprocessor architecture) and a decision subsystem (scheduling method). The action model is a translation of the previous knowledge model in a programming language or in a mathematical formalism. We propose in this paper two kinds of action models: a stochastic simulation model and a markovian model. These models are dedicated to dynamic task allocation between identical processors without communi cation cost between tasks. It is to be remarked that these action models are automatically deduced from the corresponding knowledge models. Finally, we report some results obtained from these two action models. In particular, we highlight that these two independent models return identical results and so validate them selves.

&lt;p&gt;This paper demonstrates the pontential of verification based on state spaces reduced by equivalence relations. The basic observation is that quite often, some states of a system are similar, i.e., they induce similar behaviours. Similarity can be formally expressed by defining equivalence relations on the set of states and the set of actions of a system under consideration. A state space can be constructed, in which the nodes correspond to equivalence classes of states and the arcs correspond to equivalence classes of actions. Such a state space is often much smaller than the ordinary full state space, but does allow derivation of many verification results.&lt;/p&gt;&lt;p&gt;Other researches have taken advantage of the symmetries of systems, which induce a certain kind of equivalence. The contribution fo this paper is to show that a more general notion of equivalence is useful. As example, a communication protocol modelled in the formalism of Coloured Petri Nets is verified. Aided by a computer tool supporting state spaces with equivalence classes, significant reduction of state spaces are exhibited.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Topics&lt;/strong&gt;. State space reduction methods, equivalence vs. symmetry, High-level Petri Nets, communication protocols.&lt;/p&gt;

To transfer and practically implement academic knowledge in wider society is not straightforward, and a range of measures have been used to improve technology transfer and dissemination of research from universities. One example is the technology transfer offices (TTOs), which have been set up at almost every US research university since the Bayh-Dole Act in 1980. Most TTO operations conform to a 'patent agency' model of operation where the focus is on selling patentable inventions to industrial adopters. The success of traditional TTO operations in terms of technology transfer, economic performance, and impact on academic life has, however, been questioned. This article outlines the principles of an alternative model for university technology transfer operations. The 2g model has a wider focus which might lead to increased technology transfer including a wider number of inventions and areas than current TTO practice.

This work presents a prevention method for deadlock situations, through a synchronization rule, in interorganizational workflow processes that are locally sound, but not globally sound. Such a method considers the Petri net theory and is based on the analysis of Linear Logic proof trees. The work also presents a method for the qualitative and quantitative analysis of the interorganizational workflow model process, before and after the application of the synchronization rule used to remove deadlock situations. Following the application of the synchronization rule, those models that represent the interorganizational workflow processes that are not sound are transformed into sound models due to the replacement of certain asynchronous communication places by partially synchronous communication mechanisms. As a consequence of the application of the synchronization rule, the process may suffer minor delays, reducing the process performance. The use of Linear Logic has the greatest advantage the possibility of reusing fragments of the proof tree produced before the application of the synchronization rule. Consequently the analysis of the model is only performed in that part of the model responsible for the deadlock situation.

When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transactions based on zero-safe nets. They extend ordinary pt nets with a simple mechanism for transition synchronization. We show that the net theory developed under the two most widely adopted semantic interpretations (collective token and individual token philosophies) can be uniformly adapted to zero-safe nets. In particular, we show that each zero-safe net has two associated pt nets that represent the abstract counterparts of the modeled system according to these two philosophies. We show several applications of the framework, a distributed interpreter for zs nets based on classical net unfolding (here extended with a commit rule) and discuss some extensions to other net flavours to show that the concept of zero place provides a unifying notion of transaction for several different kinds of Petri nets.