Synthesis of Liveness-Enforcing Petri Net Supervisors Based on a Think-Globally-Act-Locally Approach and a Structurally Minimal Method for Flexible Manufacturing Systems

This paper proposes a deadlock prevention policy for flexible manufacturing systems (FMSs) based on a think-globally-act-locally approach and a structurally minimal method. First, by using the think-globally-act-locally approach, a global idle place is temporarily added to a Petri net model with deadlocks. Then, at each iteration, an integer linear programming problem is formulated to design a minimal number of maximally permissive control places. Therefore, a supervisor with a low structural complexity is obtained since the number of control places is greatly compressed. Finally, by adding the designed supervisor, the resulting net model is optimally or near-optimally controlled. Three examples from the literature are used to illustrate the proposed method

Deadlock Prevention Policy with Behavioral Optimality or Suboptimality Achieved by the Redundancy Identification of Constraints and the Rearrangement of Monitors

This work develops an iterative deadlock prevention method for a special class of Petri nets that can well model a variety of flexible manufacturing systems. A deadlock detection technique, called mixed integer programming (MIP), is used to find a strict minimal siphon (SMS) in a plant model without a complete enumeration of siphons. The policy consists of two phases. At the first phase, SMSs are obtained by MIP technique iteratively and monitors are added to the complementary sets of the SMSs. For the possible existence of new siphons generated after the first phase, we add monitors with their output arcs first pointed to source transitions at the second phase to avoid new siphons generating and then rearrange the output arcs step by step on condition that liveness is preserved. In addition, an algorithm is proposed to remove the redundant constraints of the MIP problem in this paper. The policy improves the behavioral permissiveness of the resulting net and greatly enhances the structural simplicity of the supervisor. Theoretical analysis and experimental results verify the effectiveness of the proposed method

Comparison and Evaluation of Deadlock Prevention Methods for Different Size Automated Manufacturing Systems

In automated manufacturing systems (AMSs), deadlocks problems can arise due to limited shared resources. Petri nets are an effective tool to prevent deadlocks in AMSs. In this paper, a simulation based on existing deadlock prevention policies and different Petri net models are considered to explore whether a permissive liveness-enforcing Petri net supervisor can provide better time performance. The work of simulation is implemented as follows. (1) Assign the time to the controlled Petri net models, which leads to timed Petri nets. (2) Build the Petri net model using MATLAB software. (3) Run and simulate the model, and simulation results are analyzed to determine which existing policies are suitable for different systems. Siphons and iterative methods are used for deadlocks prevention. Finally, the computational results show that the selected deadlock policies may not imply high resource utilization and plant productivity, which have been shown theoretically in previous publications. However, for all selected AMSs, the iterative methods always lead to structurally and computationally complex liveness-enforcing net supervisors compared to the siphons methods. Moreover, they can provide better behavioral permissiveness than siphons methods for small systems. For large systems, a strict minimal siphon method leads to better behavioral permissiveness than the other methods

An Iterative Approach for Collision Feee Routing and Scheduling in Multirobot Stations

This work is inspired by the problem of planning sequences of operations, as welding, in car manufacturing stations where multiple industrial robots cooperate. The goal is to minimize the station cycle time, \emph{i.e.} the time it takes for the last robot to finish its cycle. This is done by dispatching the tasks among the robots, and by routing and scheduling the robots in a collision-free way, such that they perform all predefined tasks. We propose an iterative and decoupled approach in order to cope with the high complexity of the problem. First, collisions among robots are neglected, leading to a min-max Multiple Generalized Traveling Salesman Problem (MGTSP). Then, when the sets of robot loads have been obtained and fixed, we sequence and schedule their tasks, with the aim to avoid conflicts. The first problem (min-max MGTSP) is solved by an exact branch and bound method, where different lower bounds are presented by combining the solutions of a min-max set partitioning problem and of a Generalized Traveling Salesman Problem (GTSP). The second problem is approached by assuming that robots move synchronously: a novel transformation of this synchronous problem into a GTSP is presented. Eventually, in order to provide complete robot solutions, we include path planning functionalities, allowing the robots to avoid collisions with the static environment and among themselves. These steps are iterated until a satisfying solution is obtained. Experimental results are shown for both problems and for their combination. We even show the results of the iterative method, applied to an industrial test case adapted from a stud welding station in a car manufacturing line

An Efficient Siphon-Based Deadlock Prevention Policy for a Class of Generalized Petri Nets

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S 4 PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons are max -controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness-enforcing supervisor synthesis method for S 4 PR is established

On the Performance Estimation and Resource Optimisation in Process Petri Nets

Many artificial systems can be modeled as discrete dynamic systems in which resources are shared among different tasks. The performance of such systems, which is usually a system requirement, heavily relies on the number and distribution of such resources. The goal of this paper is twofold: first, to design a technique to estimate the steady-state performance of a given system with shared resources, and second, to propose a heuristic strategy to distribute shared resources so that the system performance is enhanced as much as possible. The systems under consideration are assumed to be large systems, such as service-oriented architecture (SOA) systems, and modeled by a particular class of Petri nets (PNs) called process PNs. In order to avoid the state explosion problem inherent to discrete models, the proposed techniques make intensive use of linear programming (LP) problems

Contributions to the deadlock problem in multithreaded software applications observed as Resource Allocation Systems

Desde el punto de vista de la competencia por recursos compartidos sucesivamente reutilizables, se dice que un sistema concurrente compuesto por procesos secuenciales está en situación de bloqueo si existe en él un conjunto de procesos que están indefinidamente esperando la liberación de ciertos recursos retenidos por miembros del mismo conjunto de procesos. En sistemas razonablemente complejos o distribuidos, establecer una política de asignación de recursos que sea libre de bloqueos puede ser un problema muy difícil de resolver de forma eficiente. En este sentido, los modelos formales, y particularmente las redes de Petri, se han ido afianzando como herramientas fructíferas que permiten abstraer el problema de asignación de recursos en este tipo de sistemas, con el fin de abordarlo analíticamente y proveer métodos eficientes para la correcta construcción o corrección de estos sistemas. En particular, la teoría estructural de redes de Petri se postula como un potente aliado para lidiar con el problema de la explosión de estados inherente a aquéllos. En este fértil contexto han florecido una serie de trabajos que defienden una propuesta metodológica de diseño orientada al estudio estructural y la correspondiente corrección física del problema de asignación de recursos en familias de sistemas muy significativas en determinados contextos de aplicación, como el de los Sistemas de Fabricación Flexible. Las clases de modelos de redes de Petri resultantes asumen ciertas restricciones, con significado físico en el contexto de aplicación para el que están destinadas, que alivian en buena medida la complejidad del problema. En la presente tesis, se intenta acercar ese tipo de aproximación metodológica al diseño de aplicaciones software multihilo libres de bloqueos. A tal efecto, se pone de manifiesto cómo aquellas restricciones procedentes del mundo de los Sistemas de Fabricación Flexible se muestran demasiado severas para aprehender la versatilidad inherente a los sistemas software en lo que respecta a la interacción de los procesos con los recursos compartidos. En particular, se han de resaltar dos necesidades de modelado fundamentales que obstaculizan la mera adopción de antiguas aproximaciones surgidas bajo el prisma de otros dominios: (1) la necesidad de soportar el anidamiento de bucles no desplegables en el interior de los procesos, y (2) la posible compartición de recursos no disponibles en el arranque del sistema pero que son creados o declarados por un proceso en ejecución. A resultas, se identifica una serie de requerimientos básicos para la definición de un tipo de modelos orientado al estudio de sistemas software multihilo y se presenta una clase de redes de Petri, llamada PC2R, que cumple dicha lista de requerimientos, manteniéndose a su vez respetuosa con la filosofía de diseño de anteriores subclases enfocadas a otros contextos de aplicación. Junto con la revisión e integración de anteriores resultados en el nuevo marco conceptual, se aborda el estudio de propiedades inherentes a los sistemas resultantes y su relación profunda con otros tipos de modelos, la confección de resultados y algoritmos eficientes para el análisis estructural de vivacidad en la nueva clase, así como la revisión y propuesta de métodos de resolución de los problemas de bloqueo adaptadas a las particularidades físicas del dominio de aplicación. Asimismo, se estudia la complejidad computacional de ciertas vertientes relacionadas con el problema de asignación de recursos en el nuevo contexto, así como la traslación de los resultados anteriormente mencionados sobre el dominio de la ingeniería de software multihilo, donde la nueva clase de redes permite afrontar problemas inabordables considerando el marco teórico y las herramientas suministradas para subclases anteriormente explotadas