Petri Net Structure Research Articles

Automatic reconstruction of molecular and genetic networks from discrete time series data

We apply a mathematical algorithm which processes discrete time series data to generate a complete list of Petri net structures containing the minimal number of nodes required to reproduce the data set. The completeness of the list as guaranteed by a mathematical proof allows to define a minimal set of experiments required to discriminate between alternative network structures. This in principle allows to prove all possible minimal network structures by disproving all alternative candidate structures. The dynamic behaviour of the networks in terms of a switching rule for the transitions of the Petri net is part of the result. In addition to network reconstruction, the algorithm can be used to determine how many yet undetected components at least must be involved in a certain process. The algorithm also reveals all alternative structural modifications of a network that are required to generate a predefined behaviour.

Efficient deadlock prevention policy in automated manufacturing systems using exhausted resources

To design supervisors enforcing liveness of automated manufacturing systems (AMS), an efficient deadlock prevention policy based on the exhausted resources is proposed. This policy exploits a special structure of Petri nets in the sense that the liveness of a specific system can be guaranteed if no shared resource can be emptied. In contrast to the typical conventional policies, the explicit enumeration of either the reachable states or the siphons can be avoided. Experimental results verify the efficient implementation of the proposed policy.

Formal semantics and analysis of control flow in WS-BPEL

Web service composition refers to the creation of new (Web) services by combining functionalities provided by existing ones. A number of domain-specific languages for service composition have been proposed, with consensus being formed around a process-oriented language known as WS-BPEL (or BPEL). The kernel of BPEL consists of simple communication primitives that may be combined using control-flow constructs expressing sequence, branching, parallelism, synchronization, etc. We present a comprehensive and rigorously defined mapping of BPEL constructs onto Petri net structures, and use this for the analysis of various dynamic properties related to unreachable activities, conflicting messages, garbage collection, conformance checking, and deadlocks and lifelocks in interaction processes. We use a mapping onto Petri nets because this allows us to use existing theoretical results and analysis tools. Unlike approaches based on finite state machines, we do not need to construct the state space, and can use structural analysis (e.g., transition invariants) instead. We have implemented a tool that translates BPEL processes into Petri nets and then applies Petri-net-based analysis techniques. This tool has been tested on different examples, and has been used to answer a variety of questions.

PARTICLE PETRI NET-BASED ESTIMATION IN HYBRID SYSTEMS TO DETECT INCONSISTENCIES

Monitoring a complex system consists in analysing its behaviour and reacting to abnormal situations. In this context, we have proposed a model for hybrid systems: particle Petri nets. This model allows to represent the discrete dynamics of the system through the Petri net structure and the continuous dynamics by evolution equations associated to some places. From this model, a recursive estimation process has been defined and allows corrected numerical tokens and corrected symbolic tokens to be compared. The comparison highlights inconsistent states, i.e. the states that are unreachable from the initial state of the Petri net. Inconsistencies may reveal an abnormal situation. An application to the tracking of an airliner pilot's activity is finally presented.

Evolutionary Computing of Petri Net Structure for Cyclic Job Shop Scheduling

This paper considers Cyclic Job-Shop Scheduling Problems (CJSSP) extended from the Job-Shop Scheduling Problem (JSSP). We propose an evolutionary computing method to solve the problem approximately by generating the Petri net structure for scheduling. The crossover proposed in this paper employs structural analysis of Petri net model, that is, the crossover improves the cycle time by breaking the bottle-neck circuit obtained by solving a linear programming problem. Experimental evaluation shows the effectiveness of our approach.

Action Planning for Directed Model Checking of Petri Nets

Petri nets are fundamental to the analysis of distributed systems especially infinite-state systems. Finding a particular marking corresponding to a property violation in Petri nets can be reduced to exploring a state space induced by the set of reachable markings. Typical exploration(reachability analysis) approaches are undirected and do not take into account any knowledge about the structure of the Petri net. This paper proposes heuristic search for enhanced exploration to accelerate the search. For different needs in the system development process, we distinguish between different sorts of estimates.Treating the firing of a transition as an action applied to a set of predicates induced by the Petri net structure and markings, the reachability analysis can be reduced to finding a plan to an AI planning problem. Having such a reduction broadens the horizons for the application of AI heuristic search planning technology. In this paper we discuss the transformations schemes to encode Petri nets into PDDL. We show a concise encoding of general place-transition nets in Level 2 PDDL2.2, and a specification for bounded place-transition nets in ADL/STRIPS. Initial experiments with an existing planner are presented.

Dual Flow Nets

This paper addresses the interrelation between control and data flow in embedded system models through a new design representation, called Dual Flow Net (DFN). A modeling formalism with a very close-fitting control and data flow is achieved by this representation, as a consequence of enhancing its underlying Petri net structure. The work presented in this paper does not only tackle the modeling side in embedded systems design, but also the validation of embedded system models through formal methods. Various introductory examples illustrate the applicability of the DFN principles, whereas the capability of the model to with complex designs is demonstrated through the design and verification of a real-life Ethernet coprocessor.

Transformations of Petri Nets

The aim of this paper is an introduction to the area of Petri net transformations, a rule-based approach for dynamic changes of the net structure of Petri nets. This is especially important for the stepwise construction of Petri nets in the sense of the software development process in software engineering. The concept of Petri net transformations is based on that of graph transformations and high-level replacement systems and it is introduced within a small case study logistics.

Deadlock-Free Scheduling Strategy for Automated Production Cell

Deadlock must be avoided in a manufacturing system. In this paper, an efficient algorithm for finding a good deadlock-free schedule in a manufacturing system with enough (sufficient) or limited buffer is presented. This algorithm is based on the effective genetic algorithm (GA) search method. A formal Petri net structure is introduced, and the token player is used to assure deadlock freeness. In order to make the scheduling strategy generated by GA meet the required deadlock-free constraint, a Petri net is involved in checking the implementation of a manufacturing system during the job-scheduling process. The effectiveness and efficiency of the proposed approach is illustrated by several examples.

Clustering for Petri nets

This work builds a bridge from • clustering techniques—merging neighbouring nodes which is a key feature for software engineering and the practical applications of Petri nets—to • folding techniques—merging only transitions with transitions and places with places, preserving behaviour and allowing theoretical connections to many models of concurrency. A new category of Petri nets is introduced. Morphisms support clustering, offering attractive properties to software engineering and integrating smoothly with invariants. A computationally reasonable adjunction connects it to folding-based Petri nets, namely, to two new cocomplete and complete categories. The dichotomy of structure and behaviour of Petri nets is expressed as compatible adjunctions to behavioural categories. Finally reachability and process semantics are attached categorically and a new variant of occurrence nets is proposed as a purer image of causality and branching. This framework offers categorical support for practical applications of Petri nets.

Observability of place/transition nets

We discuss the problem of estimating the marking of a place/transition (P/T) net based on event observation. We assume that the net structure is known while the initial marking is totally or partially unknown. We give algorithms to compute a marking estimate that is a lower bound of the actual marking. The special structure of Petri nets allows us to use a simple linear algebraic formalism for estimate and error computation. The error between actual marking and estimate is a monotonically nonincreasing function of the observed word length, and words that lead to null error are said to be complete. We define several observability properties related to the existence of complete words, and show how they can be proved. To prove some of them, we also introduce a useful tool, the observer coverability graph, i.e., the usual coverability graph of a P/T net augmented with a vector that keeps track of the estimation error on each place of the net. Finally, we show how the estimate generated by the observer may be used to design a state feedback controller for forbidden marking specifications.

Synthesis of deadlock prevention supervisors using Petri nets

Given an arbitrary Petri net (PN) structure, which may have uncontrollable and unobservable transitions, the deadlock prevention procedure presented here determines a set of linear inequalities on the PN markings. When the PN is supervised so that its markings satisfy these inequalities, the supervised net is proved to be deadlock-free for all initial markings that satisfy the supervision constraints. Deadlock-freedom implies that there will always be at least one transition that is enabled in the closed-loop (supervised) system. The method is not guaranteed to ensure liveness, as it can be applied to systems that cannot be made live under any circumstances. However, for controllable and observable PNs, it is shown that, when the method ensures liveness as well, the liveness-ensuring supervisor is least restrictive. Moreover, it is shown that the method is not restrictive even for PNs in which not all transitions can be made live. The procedure allows automated synthesis of the supervisors.

Estimation of the firing frequencies in discrete and continuous Petri nets models

Production frequencies provide useful information for performance analysis, monitoring and control applications of manufacturing systems. However, such frequencies are not always measurable. In this case, they must be estimated from the observation of other variables. This paper deals with production frequencies estimation for systems modelled by discrete or continuous Petri nets. For this purpose, the content of the buffers is measured on-line with a sampling period, and the evolution equations of the model are reversed. In the case of timed Petri nets, the production frequencies estimation is obtained from the approximation of the firing sequences and in the case of continuous Petri nets it results directly from the variations of the marking vector. The exact and approximated solutions of the estimation problem are described. Accuracy of the estimation is related to measurement error, Petri net structure and sampling period. Moreover, when the estimation provides several solutions, the Petri net model is extended such that a unique solution is obtained.

A brief survey and synthesis of the roles of time in petri nets

Petri nets augmented with time are interesting models which can be used for the modelling and analysis of a wide range of concurrent discrete-event systems. In this paper, the nature of the semantics of different approaches to incorporating time in Petri nets is illustrated by examples. The paper considers the critical roles of conflict, confusion and concurrence in the formulation of execution policies. Several different methods for the analysis of timed Petri net models are also discussed. The paper then introduces a timed Petri net structure which incorporates all the other structures described.

A Multi-region Linear Logic Based Calculus for Dynamic Petri Net Structures

Object based Petri nets are becoming increasingly popular in many fields of computer science. The possibility to model real-world objects as separate Petri nets supports the need for modular design of complex systems. So far object net approaches have been based on the presumption that the object nets' structure remains unchanged in all processes. This paper sheds some light on possible extensions of high-level Petri nets to incorporate the dynamical evolution of Petri net structures. The exposition is based on the Linear Logic encoding of Petri nets ([1], [12]) and coloured Petri nets ([4]). It provides a basic semantics for modifying net structures which can be employed in a framework of nets within nets, i.e. situations where Petri nets (so-called token nets) themselves are used as tokens in an underlying environment net.

Heuristic search based on Petri net structures for FMS scheduling

A heuristic search method using Petri net structures for flexible manufacturing system (FMS) scheduling is presented. To minimize makespan, an FMS scheduling problem is formulated as finding a firing sequence from the initial state to the final state of a timed Petri net model, such that the sequence reveals the minimal cost. The reachability graph is partially generated and searched. The search process is guided by a heuristic function based on firing count vectors of the state equation, predicting the total cost. Since this heuristic search exploits the linear characteristics of the state equation, which contains sufficient global information, it can efficiently generate a near-optimal or optimal solution. To deal with large systems, the proposed algorithm exploits the concurrency information to reduce the searched state space.

Petri net dynamics-based scheduling of flexible manufacturing systems with assembly

This paper presents a heuristic search method based on Petri nets for scheduling flexible manufacturing systems with assembly (FMSA) by partially generating the reachability graph. FMSAs are modeled by two types of timed place Petri nets, called generalized symmetric (GSN) and asymmetric nets (GAN). GSN is a sub-class of GAN. The special Petri net structures of GSN and GAN allow us to efficiently solve their state equations for solutions that constitute a part of the proposed heuristic function. Considering the dynamic information of nets such as concurrency and synchronization, the part of the heuristic function is adjusted since state equation solutions may over-estimate the real cost. The adjustment is based on a lower bound of the real cost and on dynamically comparing the partial estimated cost and partial real cost during the search process. Extensive simulation study shows that in most cases this work obtain better solutions than prior work.

Mission control of the MARIUS autonomous underwater vehicle: system design, implementation and sea trials

This paper describes the design and implementation of a mission control system for the MARIUS autonomous underwater vehicle (AUV). The framework adopted for system design builds on the key concept of vehicle primitive, which is a parametrized specification of an elementary operation performed by the vehicle. Vehicle primitives are obtained by coordinating the execution of a number of concurrent system tasks, which are parametrized specifications of classes of algorithms or procedures that implement basic functionalities in an underwater robotic system. Vehicle primitives are in turn logically and temporally chained to form more abstract mission procedures, which are executed as determined by mission programs, in reaction to external events. System task design is carried out using well-established tools from continuous- or discrete-time dynamic system theory, and finite-state automata to describe their logical (event-based) interaction with vehicle primitives. The design and analysis of vehicle primitives and mission procedures build on the theory of Petri nets, which are naturally oriented towards the modeling and analysis of asynchronous concurrent discrete-event systems. Vehicle primitives and mission procedures can be developed and implemented on the vehicle's distributed computer system using the specially designed software programming environments CORAL and ATOL respectively. The first is a set of software tools that allows for graphically building a library of vehicle primitives embodied in Petri nets and running them in real time. The latter provides similar tools for mission procedure programming but relies on a reactive synchronous programming language as a way to manage the potential complexity introduced by the occurrence of large Petri net structures. Whereas the first has been fully implemented, the latter has been specified but is still under development. Thus, at this stage of development, mission procedures and mission programs are effectively embodied into higher-level Petri net structures that control the scheduling of the vehicle primitives that are necessary to execute a given mission. The paper provides a summary of the general methodology adopted for the design and implementation of mission control systems for underwater robots and describes its application to the control of the MARIUS AUV. The paper introduces the experimental set-up for mission programming, mission execution and mission follow-up from a support station and describes the sequence of steps involved in programming and running a selected mission with the vehicle at sea.

Analysis of Deadlock and Circular Waits Using a Matrix Model for Flexible Manufacturing Systems

The problem of deadlock in a large class of reentrant flowline systems is analysed based on a Petri net model. The relation between deadlock and circular waits is established by rigorously defining the situation of circular blocking. Deadlock analysis is then performed in terms of circular waits and their associated structures, the so-called critical siphons and critical subsystems. A dynamical system representation obtained by coupling the Petri net marking transition equation with the matrix rule-based controller equations is adopted. The task of computing the Petri net structures of deadlock analysis is largely simplified (operations involved are of polynomial complexity) by using the matrices of this system description. An on-line maximally permissive control policy for deadlock avoidance (MAXWIP) is then devised. This can be efficiently implemented by incorporating the “outer-loop” control decisions via certain dispatching control inputs. The result is a dispatching control with deadlock avoidance, which is a generalized kanban scheme.

Hierarchical Distributed Scheduling Algorithm for Large Scale Manufacturing Systems

In this paper, we propose a hierarchical dynamic scheduling method with a strategic level scheduler and some operational level distributed schedulers. A manufacturing system is represented by hierarchical structure of Petri-Net. The strategic level scheduler makes a global schedule using a reduced manufacturing model. Each of the operational level schedulers make a real-time schedule concurrently. Results of simulation study is shown.