Timed Petri Net Model Research Articles

Petri Net Model Predictive Control Method for Batch Chemical Systems

In order to address the problem of the real-time scheduling and control of batch chemical systems, this work proposes a model predictive control method based on Petri nets. First, a method is presented to construct a batch chemical system’s timed Petri net model. Second, a control structure is designed to augment the Petri net model to control the valves. This results in timed Petri nets that formally represent the process specifications of a batch chemical system. Third, a model predictive control method is developed to schedule and control timed Petri nets, where a proposed heuristic function is utilized to perform the optimization computation. The model parameters are dynamically adjusted using online data, and both scheduling and valve control instructions are calculated in real time. Finally, a series of experiments is carried out in a beer canning plant to verify the proposed method. According to the experimental results, the scheduling and control problem can be solved in real time, where the online computations can be performed in milliseconds, and the resulting scheduling strategies are optimal or near-optimal.

An Internet-of-Things-Based Dynamic Scheduling Optimization Method for Unreliable Flexible Manufacturing Systems under Complex Operational Conditions

The dynamic scheduling problem (DSP) in unreliable flexible manufacturing systems (UFMSs) with concurrency, conflicts, resource sharing, and sequential operations is a complex optimization problem that requires the use of efficient solution methodologies. The effectiveness of scheduling UFMSs relies on the quality of equipment maintenance. Currently, UFMSs with consistently large queues of parts awaiting service employ a repair-after-failure approach as a standard maintenance procedure. This method may require unexpected resources, incur costs, consume time, and potentially disrupt the operations of other UFMSs, either partially or fully. This study suggests using a predictive maintenance (PdM) strategy that utilizes the Internet of Things (IoT) to predict and avoid early mechanical equipment failures before they happen in UFMSs, thereby reducing unplanned downtime and enhancing reliability. Therefore, the objective of this paper is to construct timed Petri net (TPN) models using the IoT for the PdM configuration of mechanical equipment in the dynamic scheduling problem of UFMSs. This necessitates that users represent the specific problem using TPNs. The process of PN modeling requires the utilization of domain knowledge pertaining to the target problems as well as to machine information. However, it is important to note that the modeling rules for PNs are straightforward and limited in number. Consequently, the TPN model is applied to generate and formulate mixed-integer linear programming (MILP) instances accurately. This is done to identify the optimal production cycle time, which may be implemented in real-life scenarios. Several UFMS instances are used to demonstrate the applications and effectiveness of the proposed method. The computational results demonstrate that the proposed method shows superior solution quality, effectively solves instances for a total of 10 parts and 6 machines, and achieves a solution in a reasonable CPU time.

Dynamic Slicing of Time Petri Net Based on MTL Property

The time Petri net (TPN) is a powerful tool for modeling, simulating, and verifying real-time systems. Unfortunately, the state spaces of the time Petri net grow exponentially due to the complexity of real-time systems. The enormous size of the state spaces could also cause state explosion problems in model checking. This paper proposes an alternative dynamic slicing algorithm written as a metric temporal logic (MTL) formula to reduce the size of the time Petri net model by considering specific criteria. Our algorithm proposes an alternative dependency graph representing the global firing time interval of the transition to remove the transitions that are never fired and do not affect the state space. The dynamic slicing algorithm involves the initial marking and the properties of the target metric temporal logic formula. Unlike the unsliced time Petri net, the result preserves all necessary execution paths for the model checking of a particular metric temporal logic formula. Therefore, model checking can generate sufficient state space to conduct verification equivalent to the unsliced time Petri net but may take less time, including if the unsliced time Petri net causes state space explosion.

Expressiveness and analysis of Delayable Timed Petri Net*

We consider an extension of Timed Petri Nets “à la Ramchandani” where the transitions are partitioned into delayable and non-delayable transitions which has proven to be suitable for the design of synchronous circuits. For this model called Delayable Timed Petri Net (DTPN), the firing delay of a non-delayable transition is strict whereas a delayable transition can miss its firing delay. Since the delays are natural numbers, this model can be studied as a discrete time model.We deal with the expressiveness of DTPN by a comparison with the well known Merlin's Time Petri Net model for which transitions can fire in a time interval. We show that DTPN are strictly more expressive w.r.t. weak timed bisimilarity than Merlin's model under the discrete-time semantics. We then deal with the symbolic reachability analysis of DTPN, for which we show the complexity of the successor symbolic state computation to be O(n). In addition, we propose a reduction of the number of edges to explore that preserves the markings and the firing sequences. The symbolic state space exploration is implemented in a prototype tool, which is evaluated on a classical TPN problem and a circuit design application.

Availability estimation in photovoltaic generation systems using Timed Petri Net simulation models

In solar photovoltaic (PV) power generation systems, availability impacts directly on annual energy production capacity. In order to reveal availability levels, the system is usually constructed and monitored. Besides to be expensive and time consuming, this approach fails to provide in-advance estimations that could benefit planning, dimensioning, and predictive maintenance. This paper proposes a Petri Net-based model that can anticipate, within a short period of time and acceptable level of accuracy, availability levels for PV systems with different sizes, architectures, generation profiles, and stages of construction. By receiving a set of offline input parameters, the model can be exploited in advance, before actually constructing the real infrastructure to be measured. Simulations show that the system behavior under variability can be anticipated with reasonable accuracy, which tends to be valuable for predictive engineering. A real PV system model illustrates our approach.

Transformation of sequence diagram to timed Petri net using Atlas Transformation Language metamodel approach

AbstractReal‐time systems are complex and composed of time‐bounded events that must satisfy the real‐time constraints for their proper functioning. To cope with the complexity of real‐time systems, model‐driven approaches such as model‐driven architecture (MDA) can be followed, which uses the conceptual models for system representation. This paper presents an MDA‐based automated approach for an early stage performance evaluation and verification of a real‐time system using the Unified Modeling Language (UML)/Modeling and Analysis of Real‐Time and Embedded systems (MARTE) sequence diagram. A metamodel‐based model‐to‐model transformation technique is used for mapping the UML/MARTE sequence diagram into the generalized Petri Net Markup Language (PNML) representation of the timed Petri net model using Atlas Transformation Language (ATL). The derived PNML representation has the advantage to support the interoperability between different Petri net tools when compared over the existing methods that produce tool‐specific representation. The proposed approach enables the system designers to create and evaluate alternate system designs and predict their behavior, contributing to improving the system quality. The contribution of the proposed technique for identifying the optimal system design is analyzed using a real‐time embedded sensor application. The proposed transformation approach is also validated using a real‐time system from the manufacturing domain.

An approach for enforcing a class of GMECs on time Petri nets with uncontrollable transitions

Real-time control is of great significance for practical plants such as intelligent manufacturing systems and transportation systems, and timing information should be integrated in their discrete models. The existing specifications expressed by generalized mutual exclusion constraints (GMECs) do not consider timing specifications in the control design of these models, which would be restrictive for the control specifications of a timed system. In the framework of time Petri net (TPN) models, this paper introduces a class of GMECs, called time GMECs (TGMECs), in which each GMEC is associated with a restricted time interval. By restricting the firing intervals of controllable transitions, an efficient method based on control functions is proposed to implement TGMECs on a TPN system in presence of uncontrollable transitions. The core of the reported method is to employ the transitions-related timing constraints in a partial modified state class graph (PMSCG) to solve mathematical programming problems. Such a PMSCG is a graph recently introduced to enhance the supervisor permissiveness for a TPN system with GMECs. In particular, the terminal condition for the construction of a PMSCG is modified. By taking advantage of the PMSCG, an online control procedure is presented to implement the supervision for TGMECs in a maximally permissive way.

An UML Based Performance Evaluation of Real-Time Systems Using Timed Petri Net

Performance is a critical non-functional parameter for real-time systems and performance analysis is an important task making it more challenging for complex real-time systems. Mostly performance analysis is performed after the system development but an early stage analysis and validation of performance using system models can improve the system quality. In this paper, we present an early stage automated performance evaluation methodology to analyse system performance using the UML sequence diagram model annotated with modeling and analysis of real-time and embedded systems (MARTE) profile. MARTE offers a performance domain sub-profile that is used for representing real-time system properties essential for performance evaluation. In this paper, a transformation technique and transformation rules are proposed to map the UML sequence diagram model into a Generalized Stochastic Timed Petri net model. All the transformation rules are implemented using a metamodel based approach and Atlas Transformation Language (ATL). A case study from the manufacturing domain a Kanban system is used for validating the proposed technique.

Efficient Approach to Scheduling of Transient Processes for Time-Constrained Single-Arm Cluster Tools With Parallel Chambers

In wafer manufacturing, extensive research on the operations of cluster tools under the steady state has been reported. However, with the shrinking down of wafer lot size, such tools are frequently required to switch from handling one lot of wafers to another, resulting in more transient processes, including start-up and close-down ones. Also, wafer residency time constraint is critical for many wafer fabrication processes. To cope with the transient scheduling problem of time-constrained single-arm cluster tools with parallel chambers, based on a generalized backward strategy, this paper first builds timed Petri net models for these two transient processes. Then, two linear programs are derived for the first time to search a feasible schedule with a minimal makespan. Two industrial examples are given to demonstrate the effectiveness of the obtained results at last.

A study of the layout planning of plant facility based on the timed Petri net and systematic layout planning.

The purpose of this research is to solve the problems of unreasonable layout of the production plant, disorder of the logistics process, and unbalanced production line in discrete manufacturing plants. By analyzing the production process and characteristics, the timed Petri net model is constructed according to the function and connection of each production unit, which is then used to generate a FlexSim simulation model of the production plant logistics system with a simulation software. Therewith the FlexSim simulation model is used to simulate the original layout of the plant, and to analyse the simulation data synthetically to put forward an improvement strategy. Combined with the use of the systematic layout planning method to analyze the overall layout of the plant and logistics relations, we infer the relevant drawings between the production units and determine the improved layout of the facilities. Finally, by comparing the before and after improvement simulation results, it is verified that the combination of timed Petri nets and systematic layout planning is effective to ameliorate the layout of the plant facilities and the logistics system. This method makes up for the factors that traditional methods have not considered, achieves the goal of reducing the cross circuitous route of the plant and the idle rate of equipment, and improving the efficiency of production.

Optimal Supervisory Control of Two Phases Intersection Using Hybrid-based Model Approach

In the present paper, a hybrid approach that combines modular modelling and Timed Petri Nets model is proposed, the main interest of this combination is to ensure optimal supervisory control of urban traffic flows in two phases intersections of medium-sized cities. Each intersection is considered as a multi-agent system, composed of all agents who represent all physical spaces. The behaviours of interconnected agents are supervised by the Timed Petri Nets model that controls the traffic light cycles according to an optimal timing plan defined by the Continuous Genetic Algorithm. A real two phases intersection in Sidi Bel-Abbes City is presented as an example. The proposed timing plan is compared with the current one using SUMO software for the most important objective functions. Also, the proposed model's behaviour is compared with TSIS-CORSIM software's model, and all obtained experiments results show the effectiveness of the approach and its possibility to be extended and applied to a many-phases intersection.

Modeling and Analyzing of Emergency Vehicle Preemption in a Four-phase Intersection via TPN

Emergency vehicles (EVs) play an important role in public service. And the EV’s timeliness and safety are very important. Focusing on the switch of the phases in a four-phase intersection, this paper presents a novel phase-changing model based on timed Petri nets (TPNs) for the traffic light system and proposes a method that uses TPNs to model the preemption of emergency vehicles in such an intersection. Our model ignores many actual details. By controlling the phases, our method ensures that the EVs can pass through the intersection with no or less delay, and the safety of the traffic model on emergency scene can be ensured. To our knowledge, we are the first to employ TPNs to model EV system on a four-phase intersection. The liveness and reversibility of such a TPN model are also verified through the reachability graph of the TPN.

Formal Analysis of Emergency Department Staffing Based on Stochastic Timed Petri Net Models

Abstract Appropriate staffing of an emergency department (ED) is not only essential to the delivery of quality care to patients, but also critical to the profitability of the ED. Current practice of ED staffing is largely based on patient flow observation and the rule of thumb. This paper attempts to use stochastic timed Petri nets (STPN) to formally model the workflow of an ED and then analyze the impact of staffing to the performance of the care service on various patient volumes and acuity profiles. An STPN tool is developed to aid appropriate staffing that aligns staffing and demand.

A measure of mental workload during multitasking: Using performance-based Timed Petri Nets

Multitasking is common in emergency, which will result in man-made error due to many factors such as inappropriate Mental Workload (MW). To improve the performance under multitasking, the automatic equipment or assistive systems carry out task/interface optimizations according to the MW evaluation results, and the effectiveness of these technologies depends on how to choose an appropriate MW evaluation model. This paper has developed a performance-based Timed Petri Nets (TPN) model to evaluate MW during multitasking. The concrete functioned places and transitions, were proposed to structure a human resource allocation and recovery processes in TPN. The characteristics of operator are interpreted as initial markings of places and delay of transitions. Task performance is calculated as the difference between the triggering time of two transitions and a behavior process structure, respectively. The real-time MW is quantified and expressed as the remaining percentage of tokens in the attention resource place. A case study of triple-task execution was examined for verification of the model. Furthermore, the distinguishability and stability of the model, its comparison with ACT-R, and the application in task optimization were discussed. Relevance to industryThe Timed Petri Nets-based model can analyse the influence between mental workload and system states while proposed quantitative and individualized results of mental workload, which can direct a mental workload-based task optimization in safety-critical systems under multitasking in the design phase.

Evaluation of the performance of an automated metallographic samples analysis system by means of Petri Nets modelling

This paper presents the results of the research about the automation of the metallographic samples preparation and analysis processes. At the University of Oradea the authors designed and made an automated metallographic samples preparation and analysis system. This automated system can achieve polishing, attack by reagents and metallographic analysis. The flexible cell (the automated system) is made of two subsystems. The first subsystem, which is served by an industrial robot, performs the polishing and the sample surface assessment. The second subsystem, also served by an industrial robot, performs the reagent attack and finishes the metallographic analysis in order to determine the microstructure of the sample. The authors have designed a timed Petri nets model in order to assess the performance of the automated system and to identify the possible bottlenecks. The model is made for the case that the system is required to analyse two kinds of samples. The sequences performed by the industrial robots are modelled by transitions with associated timings that are equal to the real time periods taken by the robots to execute the corresponding actions. Other activities, such as grinding polishing, finishing polishing, reagent attack, washing, microscope examining, have been also modelled by means of transitions. The execution of a transition (the completion of a real sequence) is possible if certain conditions are met. These conditions are modelled into the Petri net by means of positions. The number of samples that can be analyzed in a certain time period can be determined by simulation.

The Ant Colony Algorithm Based on Logic Time Petri Nets and Application in Electronic-Commerce Logistics

Based on Logic Time Petri nets (LTPNs) models, this paper focuses on improving the efficiency of Petri Net intelligent search method execution. With an analysis of the E-Commerce Logistics (ECL) system, the method of system scheduling using LTPNs is studied, and the Ant Colony algorithm is proposed based on it. By introducing the concept of pheromones to system transition, using the Ant Colony algorithm (ACA) in the processing of the network, and setting the heuristic factor in combination with the time boundary, the non-deterministic behavior can be automatically analyzed and selected in the LTPNs so that the efficiency of control and scheduling during the system dynamics operation is improved. The result of the analysis of the ECL system serves as evidence of the superiority of ACA.

An Efficient Deadlock Prevention Policy for Noncyclic Scheduling of Multicluster Tools

Scheduling of multicluster tools has received much attention due to its complexity of interaction among cluster tools. A cluster tool comprises several modules such as processing modules, a transfer module with a single or dual-armed handling robot, and loadlock modules. A multicluster tool comprises two, three, or more cluster tools that are interconnected with each other. In this paper, we propose a deadlock prevention policy for noncyclic scheduling of dual-armed multicluster tools. The proposed deadlock prevention policy is effective for generating an efficient schedule for two or three-connected multicluster tools with a single or a dual-path flow. This is proven by analyzing the strict minimal siphon of the Petri net model. The performance of the proposed method is compared with that of a maximal permissible deadlock prevention policy. The results demonstrate that the proposed method is computationally efficient for larger state spaces and more suitable than conventional deadlock prevention policies for generating effective schedules for noncyclic scheduling of multicluster tools. Note to Practitioners —Scheduling of multicluster tools has recently attracted attention in the growing semiconductor manufacturing industry. Most conventional studies on multicluster tools focus on cyclic scheduling to minimize cycle time with swap strategy. The challenge addressed by this paper is to derive a deadlock-free schedule for multicluster tools with noncyclic operations. We propose a simple deadlock prevention policy that can be applied to large-scale timed Petri net (PN) model of general multicluster tools without enumeration of siphon computations or solution of mixed integer programming. A timed PN model is developed for noncyclic operations of dual-armed multicluster tools with a dual ath. The computational results show that the approximately 10% of the total throughput of the proposed method is better than those of the conventional methods. It enables more efficient operations for noncyclic scheduling under transient periods including cleaning operations.

Time Petri net-based modelling of complex adaptive agent system

In order to depict internal mechanism of complex adaptive agent system and improve capabilities of computer-assisted modelling, a new modelling approach is presented by the combination of Time Petri Net (TPN) and multi-agent technology. In the methods, agent is viewed as basic modelling element and Petri net is used to describe the static rules of agent. Because of the TPN model combining the advantages of time Petri net and multi-agent technology, the state space explosion of complex adaptive agent system is prevented. As an example, the crane scheduling system is defined as complex adaptive agent system. The results that proposed system can complete scheduling task of the steel-making continuous casting and provide guidance for optimizing production systems and exploring operation mechanism.

Efficient Approach to Cyclic Scheduling of Single-Arm Cluster Tools With Chamber Cleaning Operations and Wafer Residency Time Constraint

In semiconductor manufacturing, with the shrinking down of wafer circuit widths, a strict quality control is required for wafer fabrication processes, resulting in that after a wafer being processed and removed from a chamber, a cleaning operation that takes significant time is performed for eliminating the chemical residual. Such a cleaning operation makes a traditional backward strategy for single-arm cluster tools inefficient. By the existing studies, it is shown that the productivity can be improved if some numbers of chambers at a step are kept empty. With this idea, an extended backward strategy is proposed by deciding the optimal number of empty chambers. Based on such a strategy, this paper studies the challenging problem for scheduling a single-arm cluster tool with both chamber cleaning operations and wafer residency time constraint for the first time. By building a timed Petri net model for the system, two linear programs are proposed to determine the minimal cycle time and test the existence of a feasible schedule and find it if existing. At last, two industrial examples are used to demonstrate the obtained results.

Time-Based Web Service Composition

This article describes how incorporating temporal constraints in web service composition results in more complex models and makes the verification of temporal consistency during the modeling and execution crucial. This article proposes a model named H-Service-Net based on the time petri net model to control and manage temporal consistency; the model also supports time constraints and exception handling. First, this approach proposes a modular approach for modeling composition using Extend Time Unit System, Allen's interval algebra, and comparison operators in a time petri net model to consider all types of temporal constraints. Subsequently, this article presents algorithms on checking temporal consistency and mechanism for exception handling and validating the system in an implementation tool (H-Service-Editor) based on the proposed approach that uses BizTalk Server 2013 to evaluate the implementation of temporal constraints and timeout exception handling. Finally, an exhaustive performance experiment is presented to assess the scalability of the authors' approach.