Showing papers on "Petri net published in 2017"

Verification of State-Based Opacity Using Petri Nets

Abstract: A system is said to be opaque if a given secret behavior remains opaque (uncertain) to an intruder who can partially observe system activities. This work addresses the verification of state-based opacity in systems modeled with Petri nets. The secret behavior of a system is defined as a set of states. More precisely, two state-based opacity properties are considered: current-state opacity and initial-state opacity . We show that both current-state and initial-state opacity problems in bounded Petri nets can be efficiently solved by using a compact representation of the reachability graph, called basis reachability graph (BRG). This approach is practically efficient since the exhaustive enumeration of the reachability space can be avoided.

Compact Supervisory Control of Discrete Event Systems by Petri Nets With Data Inhibitor Arcs

Abstract: This work proposes a novel structure in Petri nets, namely data inhibitor arcs, and their application to the optimal supervisory control of Petri nets. A data inhibitor arc is an arc from a place to a transition labeled with a set of integers. A transition is disabled by a data inhibitor arc if the number of tokens in the place is in the set of integers labeled on it. Its formal definitions and properties are given. Then, we propose a method to design an optimal Petri net supervisor with data inhibitor arcs to prevent a system from reaching illegal markings with respect to control specifications. Two techniques are developed to reduce the supervisor structure by compressing the number of control places. Finally, a number of examples are used to illustrate the proposed approaches and experimental results show that they can obtain optimal Petri net supervisors for the net models that cannot be optimally controlled by pure net supervisors. A significant result is that the proposed approach can always lead to an optimal supervisor with only one control place for bounded Petri nets on the premise that such a supervisor exists.

Basis Marking Representation of Petri Net Reachability Spaces and Its Application to the Reachability Problem

Abstract: In this paper, a compact representation of the reachability graph of a Petri net is proposed. The transition set of a Petri net is partitioned into the subsets of explicit and implicit transitions in such a way that the subnet induced by implicit transitions does not contain directed cycles. The firing of implicit transitions can be abstracted so that the reachability set of the net can be completely characterized by a subset of reachable markings called basis makings . We show that to determine a max-cardinality- $T_{I}$ basis partition is an NP-hard problem, but a max-set- $T_{I}$ basis partition can be determined in polynomial time. The generalized version of the marking reachability problem in a Petri net can be solved by a practically efficient algorithm based on the basis reachability graph. Finally, this approach is further extended to unbounded nets.

A Necessary and Sufficient Condition for a Resource Subset to Generate a Strict Minimal Siphon in S 4PR

Abstract: Systems of sequential systems with shared resources (S4PR) represent a class of Petri nets that have powerful modeling capability for resource allocation systems. Their efficient siphon computation is important. An open issue is how to determine whether a resource subset can generate a strict minimal siphon (SMS). This paper presents the answer. In particular, we propose a new concept called characteristic implicit resource-transition nets. By charactering such nets, we successfully establish a necessary and sufficient condition for a resource subset to generate an SMS.

Process mining using BPMN: relating event logs and process models

Abstract: Process-aware information systems (PAIS) are systems relying on processes, which involve human and software resources to achieve concrete goals. There is a need to develop approaches for modeling, analysis, improvement and monitoring processes within PAIS. These approaches include process mining techniques used to discover process models from event logs, find log and model deviations, and analyze performance characteristics of processes. The representational bias (a way to model processes) plays an important role in process mining. The BPMN 2.0 (Business Process Model and Notation) standard is widely used and allows to build conventional and understandable process models. In addition to the flat control flow perspective, subprocesses, data flows, resources can be integrated within one BPMN diagram. This makes BPMN very attractive for both process miners and business users, since the control flow perspective can be integrated with data and resource perspectives discovered from event logs. In this paper, we describe and justify robust control flow conversion algorithms, which provide the basis for more advanced BPMN-based discovery and conformance checking algorithms. Thus, on the basis of these conversion algorithms low-level models (such as Petri nets, causal nets and process trees) discovered from event logs using existing approaches can be represented in terms of BPMN. Moreover, we establish behavioral relations between Petri nets and BPMN models and use them to adopt existing conformance checking and performance analysis techniques in order to visualize conformance and performance information within a BPMN diagram. We believe that the results presented in this paper can be used for a wide variety of BPMN mining and conformance checking algorithms. We also provide metrics for the processes discovered before and after the conversion to BPMN structures. Cases for which conversion algorithms produce more compact or more complicated BPMN models in comparison with the initial models are identified.

Characterization of Admissible Marking Sets in Petri Nets With Conflicts and Synchronizations

Abstract: In this paper we study the problem of constraint transformation for Petri nets with uncontrollable transitions and containing both conflicts and synchronizations. We show that given an arbitrary net and a set of legal markings, the admissible marking set cannot always be represented by a finite number of disjunctions of GMECs. Moreover, we characterize the GMEC inflation phenomenon, that is, the case in which the representation of the admissible marking set may be too complex to be efficiently implemented in a closed-loop net. To rule out the possibility of GMEC inflation we consider a subclass of constraints called singular GMECs with an acyclic backward-conflict-free uncontrollable subnet. By these assumptions we propose an algorithm to transform a given singular GMEC into a controllable OR-GMEC which precisely characterizes its admissible marking set.

Design and Verification of Real-Life Processes With Application of Petri Nets

Abstract: This paper focuses on the design and verification methods of distributed logic controllers supervising real-life processes. Such systems have to be designed very carefully and precisely in order to operate flawlessly and to meet user needs. We propose to use interpreted Petri nets as modeling formalism. A new design flow of distributed logic controllers is introduced. The methodology covers the development process from the specification stage to the final implementation of the controller in the distributed devices. In the proposed solution, the system is decomposed into separate modules that form a distributed system. Furthermore, the specification (before and after the decomposition process) is formally verified with the application of the model checking technique against predefined behavioral requirements. Finally, the system is implemented in real devices. The usage of formal methods and double model checking ensure the correct functionality of the designed distributed logic controller. The theoretical approach is supplemented by the practical experiments. Furthermore, the proposed idea is illustrated by an example of a smart home system.

Calculation of Siphons and Minimal Siphons in Petri Nets Based on Semi-Tensor Product of Matrices

Abstract: In this paper, we address the problems of enumerating siphons and minimal siphons in ordinary Petri nets (PNs) by resorting to the semi-tensor product (STP) of matrices. First, a matrix equation, called the siphon equation (SE), is established by using STP. Second, an algorithm is proposed to calculate all siphons in ordinary PNs. An example is presented to illustrate the theoretical results and show that the proposed method is more effective than other existing methods in calculating all siphons of PNs. Third, an efficient recursion algorithm is also proposed, which can be applied to computing all minimal siphons for any ordinary PNs. Last, some results on the computational complexity of the proposed algorithms, in this paper, are provided, as well as experimental results.

Fully Expanded Tree for Property Analysis of One-Place-Unbounded Petri Nets

Abstract: This paper proposes a fully expanded tree (FET) approach for one-place-unbounded Petri nets. The FET of a one-place-unbounded Petri net consists of all and only reachable markings from its initial marking. Its applications to liveness and deadlock analysis for such Petri nets are developed. The proposed method has a larger application scope than all the existing methods for them. Several examples are provided to show its superiority over the state-of-the-art methods.

Automated guided vehicle mission reliability modelling using a combined Fault Tree and Petri net approach

Abstract: Automated guided vehicles (AGVs) are being extensively used for intelligent transportation and distribution of materials in warehouses and autoproduction lines due to their attributes of high efficiency and low costs. Such vehicles travel along a predefined route to deliver desired tasks without the supervision of an operator. Much effort in this area has focused primarily on route optimisation and traffic management of these AGVs. However, the health management of these vehicles and their optimal mission configuration have received little attention. To assure their added value, taking a typical AGV transport system as an example, the capability to evaluate reliability issues in AGVs are investigated in this paper. Following a failure modes effects and criticality analysis (FMECA), the reliability of the AGV system is analysed via fault tree analysis (FTA) and the vehicles mission reliability is evaluated using the Petri net (PN) method. By performing the analysis, the acceptability of failure of the mission can be analysed, and hence the service capability and potential profit of the AGV system can be reviewed and the mission altered where performance is unacceptable. The PN method could easily be extended to have the capability to deal with fleet AGV mission reliability assessment.

Modelling and Performance Evaluation with TimeNET 4.4

Abstract: The paper presents the current status of the software tool TimeNET. It supports modeling and performance evaluation of stochastic models, including extended deterministic and stochastic Petri nets, colored stochastic Petri nets, and Markov chains as well as UML extensions. Among its main characteristics are simulation and analysis modules for stationary and transient evaluation of Petri nets including non-exponentially distributed delays, as well as a simulation module for complex colored models. Recent enhancements include algorithms for the efficient rare-event simulation of Petri nets, a new multi-trajectory hybrid simulation/analysis algorithm, and a net class for Markov chains.

Transition Cover-Based Robust Petri Net Controllers for Automated Manufacturing Systems With a Type of Unreliable Resources

Abstract: So far, the majority of deadlock control policies for automated manufacturing systems (AMSs) are based on the assumption that no resource fails; while for AMSs with unreliable resources, the main concerns are deadlock avoidance problems. This paper focuses on the robust deadlock prevention problem for AMSs with a type of unreliable resources, and assumes that at most one of unreliable resources fails at a time. Petri net is introduced to model the considered AMS. Deadlock can be characterized in terms of maximal perfect resource transition-circuits (MPRT-circuits). To develop robust Petri net deadlock controllers with small structures for the system, a new concept of strong transition covers is presented, which is a special kind of transition covers. By designing a control place with a proper control variable to each MPRT-circuit in the strong transition cover, a 1-robust Petri net controller is obtained, whereas the control variables can be determined by an integer linear programming. Such a 1-robust controller ensures that the system can process all types of parts infinitely even if one of unreliable resources fails. Since the number of MPRT-circuits in a strong transition cover is much less than that of all MPRT-circuits, our Petri net controller is of small structural size. Each AMS with a type of unreliable resources has at least a transition cover. An algorithm is presented for checking the strongness of transition covers, and transforming weak transition covers into strong ones. Finally, some examples are given to illustrate the effectiveness of the proposed method.

On the Decidability and Complexity of Diagnosability for Labeled Petri Nets

Abstract: In this paper, we investigate the decidability and complexity of the fault diagnosis problem in unbounded labeled Petri nets. First, we show that checking diagnosability for unbounded Petri nets is decidable. We present a new necessary and sufficient condition for diagnosability, which can be reduced to a model checking problem for unbounded Petri nets. Then, we show that checking diagnosability for unbounded Petri nets is EXPSPACE-complete. This complexity result is further extended to various subclasses of Petri nets. To the best of our knowledge, this is the first paper that establishes decidability and complexity results for diagnosability of unbounded Petri nets.

An improved approach to test diagnosability of bounded petri nets

Abstract: For bounded Petri nets, Cabasino et al. propose a diagnosability test method that is based on the analysis of a modified basis reachability graph and a basis reachability diagnoser. However, its complexity is exponential in the number of nodes of the basis reachability diagnoser. In order to reduce the complexity of their method, this paper presents a new diagnosability test approach for bounded Petri nets. We present the concept of an extended basis reachability graph and prove that our approach is of polynomial complexity in the number of nodes of extended basis reachability graphs. An example is given to illustrate the application of the presented approach.

Petri-Net Controller Synthesis for Partially Controllable and Observable Discrete Event Systems

Abstract: To enforce linear constraints on Petri nets that are partially controllable and observable, this work proposes an approach based on constraint transformation. First, a state-space equation of a Petri net control system based on event feedback is obtained by expressing a control action as a matrix, and the optimal control policy is designed. However, this policy needs to solve a nonlinear program on line. Second, pre-transition-gain-transformation is proposed to equivalently transform a constraint into a disjunction of new ones for an uncontrollable transition, and, similarly, post-transition-gain-transformation to transform a constraint into a disjunction of new ones for an unobservable transition. An algorithm is then given to transform a constraint into a disjunction of admissible ones, and, consequently, an efficient policy, which may not be optimal, can be designed. Third, in order to guarantee that the policy be both efficient and optimal, a dynamic linear constraint is introduced. Further, observing-transformation is proposed to simplify a dynamic constraint for an unobservable transition, and an algorithm is given to equivalently transform a class of linear constraints into admissible dynamic ones. As a result, an optimal controller requiring little online computation can be designed accordingly for some class of Petri nets. Finally, a maze system is used to illustrate the theoretical results.

Formal modeling and control of cyber-physical manufacturing systems:

Abstract: Cyber-physical manufacturing systems are a new paradigm of manufacturing systems that integrate cyber systems and physical systems to aid smart manufacturing. Cyber-physical manufacturing systems can improve agility and responsiveness and guarantee the quality of products to meet the market requirements. Meanwhile, cyber-physical manufacturing systems also become susceptible to cyber-attacks. In order to improve the trustworthiness of cyber-physical manufacturing systems in the dynamic modeling phase, a cyber-physical manufacturing system formal model based on object-oriented Petri nets is presented from the perspective of multi-agent systems. Some mathematical methods and supporting tools of Petri nets can be utilized to analyze, verify, and validate cyber-physical manufacturing system formal model. To defense the malicious software spreading in cyber-physical manufacturing systems at run-time, a spreading dynamics model is proposed, and its dynamic behaviors are analyzed. A hybrid bifurcation control me...

A Black-Box Identification Method for Automated Discrete-Event Systems

Abstract: This paper deals with the identification of discrete-event manufacturing systems that are automated using a programmable logic controller (PLC). The behavior of the closed-loop system (PLC and Plant) is observed during its operation and is represented by a single long sequence of observed input/output (I/O) signals vectors. The proposed method follows a black-box and passive identification approach that allows addressing large and complex industrial DES and yields compact and expressive interpreted Petri net (IPN) models. It consists of two complementary stages; the first one obtains, from the I/O sequence, the reactive part of the model composed by observable places and transitions. The I/O sequence is also mapped into a sequence of the created transitions, from which the second stage builds the non observable part of the model including places that ensure the reproduction of the observed input output sequence. This method, based on polynomial-time algorithms on the size of the input data, has been implemented as a software tool that generates and draws the IPN model; it has been tested with input/output sequences obtained from real systems in operation. The tool is described and its application is illustrated through a case study.

A Timed Colored Petri Net Simulation-Based Self-Adaptive Collaboration Method for Production-Logistics Systems

Abstract: Complex and customized manufacturing requires a high level of collaboration between production and logistics in a flexible production system. With the widespread use of Internet of Things technology in manufacturing, a great amount of real-time and multi-source manufacturing data and logistics data is created, that can be used to perform production-logistics collaboration. To solve the aforementioned problems, this paper proposes a timed colored Petri net simulation-based self-adaptive collaboration method for Internet of Things-enabled production-logistics systems. The method combines the schedule of token sequences in the timed colored Petri net with real-time status of key production and logistics equipment. The key equipment is made ‘smart’ to actively publish or request logistics tasks. An integrated framework based on a cloud service platform is introduced to provide the basis for self-adaptive collaboration of production-logistics systems. A simulation experiment is conducted by using colored Petri nets (CPN) Tools to validate the performance and applicability of the proposed method. Computational experiments demonstrate that the proposed method outperforms the event-driven method in terms of reductions of waiting time, makespan, and electricity consumption. This proposed method is also applicable to other manufacturing systems to implement production-logistics collaboration.

Modeling and Analysis of the Thermal Properties Exhibited by Cyberphysical Data Centers

Abstract: Data centers (DCs) contribute toward the prevalent application and adoption of the cloud by providing architectural and operational foundation. To perform sustainable computation and storage, a DC is equipped with tens of thousands of servers, if not more. It is worth noting that the operational cost of a DC is being dominated by the cost spent on energy consumption. In this paper, we model a DC as a cyberphysical system (CPS) to capture the thermal properties exhibited by the DC. All software aspects, such as scheduling, load balancing, and all the computations performed by the devices, are considered the “cyber” component. The supported infrastructure, such as servers and switches, are modeled as the “physical” component of the CPS. We perform detailed modeling of the thermal characteristics displayed by the major components of the CPS. Moreover, we propose a thermal-aware control strategy that uses a high-level centralized controller and a low-level centralized controller to manage and control the thermal status of the cyber components at different levels. Our proposed strategy is testified and demonstrated by executing on a real DC workload and comparing it with three existing strategies, i.e., one classical and two thermal-aware strategies. Furthermore, we also perform formal modeling, analysis, and verification of the strategies using high-level Petri nets, the Z language, the Satisfiability Modulo Theories Library (SMT-Lib), and the Z3 solver.

Petri games: Synthesis of distributed systems with causal memory

Abstract: We present a new multiplayer game model for the interaction and the flow of information in a distributed system. The players are tokens on a Petri net. As long as the players move in independent parts of the net, they do not know of each other; when they synchronize at a joint transition, each player gets informed of the causal history of the other player. We show that for Petri games with a single environment player and an arbitrary bounded number of system players, deciding the existence of a safety strategy for the system players is EXPTIME-complete.

Diagnosability Analysis of Labeled Time Petri Net Systems

Abstract: In this paper, we focus on two notions of diagnosability for labeled Time Petri net (PN) systems: $K$ -diagnosability implies that any fault occurrence can be detected after at most $K$ observations, while $\tau$ -diagnosability implies that any fault occurrence can be detected after at most $\tau$ time units. A procedure to analyze such properties is provided. The proposed approach uses the Modified State Class Graph, a graph the authors recently introduced for the marking estimation of labeled Time PN systems, which provides an exhaustive description of the system behavior. A preliminary diagnosabilty analysis of the underlying logic system based on classical approaches taken from the literature is required. Then, the solution of some linear programming problems should be performed to take into account the timing constraints associated with transitions.

A Petri-Net-based modelling approach to railway bridge asset management

Abstract: Management of a large portfolio of infrastructure assets is a complex and demanding task for transport agencies. Although extensive research has been conducted on probabilistic models for asset management, in particular bridges, focus has been almost exclusively on deterioration modelling. The model being presented in this study tries to reunite a disjointed system by combining deterioration, inspection and maintenance models. A Petri-Net modelling approach is employed and the resulting model consists of a number of different modules each with its own source of data, calibration methodology and functionality. The modules interconnect providing a robust framework. The interaction between the modules can be used to provide meaningful outputs useful to railway bridge portfolio managers.

Detecting Data Inconsistency Based on the Unfolding Technique of Petri Nets

Abstract: The errors of data inconsistency occur in a concurrent system when some concurrent operations are conducted improperly. The model-checking technique is widely used to detect them based on the state transition graph. However, the state space explosion problem is the biggest obstacle for this technique, since the state transition graph is based on the interleaving semantics that can result in a rapid increase of the graph scale. In addition, data inconsistency is closely related with concurrent operations, but the state transition graph hardly characterizes concurrency due to its interleaving semantics. The unfolding technique of Petri nets can both alleviate the state explosion and characterize concurrency because it is based on the concurrent semantics. In this paper, we define Petri net with data to model concurrent systems with three kinds of data operations: read , write, and delete , and then formalize data inconsistency . We propose an unfolding method to produce a finite complete prefix (FCP) for each PD-net. Then, a matrix that represents all concurrency relations of transitions is constructed in view of FCP. Furthermore, the error of data inconsistency can be detected via this matrix. The related algorithms and the developed tool are introduced, and experiments illustrate their effectiveness and advantages. An example of industrial information system shows the usefulness of our study.