1,400 research outputs found

    Elasticity and Petri nets

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    Digital electronic systems typically use synchronous clocks and primarily assume fixed duration of their operations to simplify the design process. Time elastic systems can be constructed either by replacing the clock with communication handshakes (asynchronous version) or by augmenting the clock with a synchronous version of a handshake (synchronous version). Time elastic systems can tolerate static and dynamic changes in delays (asynchronous case) or latencies (synchronous case) of operations that can be used for modularity, ease of reuse and better power-delay trade-off. This paper describes methods for the modeling, performance analysis and optimization of elastic systems using Marked Graphs and their extensions capable of describing behavior with early evaluation. The paper uses synchronous elastic systems (aka latency-tolerant systems) for illustrating the use of Petri nets, however, most of the methods can be applied without changes (except changing the delay model associated with events of the system) to asynchronous elastic systems.Peer ReviewedPostprint (author's final draft

    Optimal trajectory generation for Petri nets

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    Recently, the increasing complexity of IT systems requires the early verification and validation of the system design in order to avoid the costly redesign. Furthermore, the efficiency of system operation can be improved by solving system optimization problems (like resource allocation and scheduling problems). Such combined optimization and validation, verification problems can be typically expressed as reachability problems with quantitative or qualitative measurements. The current paper proposes a solution to compute the optimal trajectories for Petri net-based reachability problems with cost parameters. This is an improved variant of the basic integrated verification and optimization method introduced in [11] combining the efficiency of Process Network Synthesis optimization algorithms with the modeling power of Petri nets

    Abstract Dependency Graphs for Model Verification

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    Scheduling and discrete event control of flexible manufacturing systems based on Petri nets

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    A flexible manufacturing system (FMS) is a computerized production system that can simultaneously manufacture multiple types of products using various resources such as robots and multi-purpose machines. The central problems associated with design of flexible manufacturing systems are related to process planning, scheduling, coordination control, and monitoring. Many methods exist for scheduling and control of flexible manufacturing systems, although very few methods have addressed the complexity of whole FMS operations. This thesis presents a Petri net based method for deadlock-free scheduling and discrete event control of flexible manufacturing systems. A significant advantage of Petri net based methods is their powerful modeling capability. Petri nets can explicitly and concisely model the concurrent and asynchronous activities, multi-layer resource sharing, routing flexibility, limited buffers and precedence constraints in FMSs. Petri nets can also provide an explicit way for considering deadlock situations in FMSs, and thus facilitate significantly the design of a deadlock-free scheduling and control system. The contributions of this work are multifold. First, it develops a methodology for discrete event controller synthesis for flexible manufacturing systems in a timed Petri net framework. The resulting Petri nets have the desired qualitative properties of liveness, boundedness (safeness), and reversibility, which imply freedom from deadlock, no capacity overflow, and cyclic behavior, respectively. This precludes the costly mathematical analysis for these properties and reduces on-line computation overhead to avoid deadlocks. The performance and sensitivity of resulting Petri nets, thus corresponding control systems, are evaluated. Second, it introduces a hybrid heuristic search algorithm based on Petri nets for deadlock-free scheduling of flexible manufacturing systems. The issues such as deadlock, routing flexibility, multiple lot size, limited buffer size and material handling (loading/unloading) are explored. Third, it proposes a way to employ fuzzy dispatching rules in a Petri net framework for multi-criterion scheduling. Finally, it shows the effectiveness of the developed methods through several manufacturing system examples compared with benchmark dispatching rules, integer programming and Lagrangian relaxation approaches

    On Minimum-time Control of Continuous Petri nets: Centralized and Decentralized Perspectives

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    Muchos sistemas artificiales, como los sistemas de manufactura, de logística, de telecomunicaciones o de tráfico, pueden ser vistos "de manera natural" como Sistemas Dinámicos de Eventos Discretos (DEDS). Desafortunadamente, cuando tienen grandes poblaciones, estos sistemas pueden sufrir del clásico problema de la explosión de estados. Con la intención de evitar este problema, se pueden aplicar técnicas de fluidificación, obteniendo una relajación fluida del modelo original discreto. Las redes de Petri continuas (CPNs) son una aproximación fluida de las redes de Petri discretas, un conocido formalismo para los DEDS. Una ventaja clave del empleo de las CPNs es que, a menudo, llevan a una substancial reducción del coste computacional. Esta tesis se centra en el control de Redes de Petri continuas temporizadas (TCPNs), donde las transiciones tienen una interpretación temporal asociada. Se asume que los sistemas siguen una semántica de servidores infinitos (velocidad variable) y que las acciones de control aplicables son la disminución de la velocidad del disparo de las transiciones. Se consideran dos interesantes problemas de control en esta tesis: 1) control del marcado objetivo, donde el objetivo es conducir el sistema (tan rápido como sea posible) desde un estado inicial a un estado final deseado, y es similar al problema de control set-point para cualquier sistema de estado continuo; 2) control del flujo óptimo, donde el objetivo es conducir el sistema a un flujo óptimo sin conocimiento a priori del estado final. En particular, estamos interesados en alcanzar el flujo máximo tan rápido como sea posible, lo cual suele ser deseable en la mayoría de sistemas prácticos. El problema de control del marcado objetivo se considera desde las perspectivas centralizada y descentralizada. Proponemos varios controladores centralizados en tiempo mínimo, y todos ellos están basados en una estrategia ON/OFF. Para algunas subclases, como las redes Choice-Free (CF), se garantiza la evolución en tiempo mínimo; mientras que para redes generales, los controladores propuestos son heurísticos. Respecto del problema de control descentralizado, proponemos en primer lugar un controlador descentralizado en tiempo mínimo para redes CF. Para redes generales, proponemos una aproximación distribuida del método Model Predictive Control (MPC); sin embargo en este método no se considera evolución en tiempo mínimo. El problema de control de flujo óptimo (en nuestro caso, flujo máximo) en tiempo mínimo se considera para redes CF. Proponemos un algoritmo heurístico en el que calculamos los "mejores" firing count vectors que llevan al sistema al flujo máximo, y aplicamos una estrategia de disparo ON/OFF. También demostramos que, debido a que las redes CF son persistentes, podemos reducir el tiempo que tarda en alcanzar el flujo máximo con algunos disparos adicionales. Los métodos de control propuestos se han implementado e integrado en una herramienta para Redes de Petri híbridas basada en Matlab, llamada SimHPN

    Synthesis of asynchronous controllers using integer linear programming

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    A novel strategy for the logic synthesis of asynchronous control circuits is presented. It is based on the structural theory of Petri nets and integer linear programming. Techniques that are capable of checking implementability conditions, such as complete state coding, and deriving a gate netlist to implement the specified behavior are presented. These techniques can handle Petri net specifications consisting of several thousands of transitions and provide a significant speed-up compared with techniques that have previously been proposed.Peer ReviewedPostprint (published version

    Performance Bounds for Synchronized Queueing Networks

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    Las redes de Petri estocásticas constituyen un modelo unificado de las diferentes extensiones de redes de colas con sincronizaciones existentes en la literatura, válido para el diseño y análisis de prestaciones de sistemas informáticos distribuidos. En este trabajo se proponen técnicas de cálculo de cotas superiores e inferiores de las prestaciones de redes de Petri estocásticas en estado estacionario. Las cotas obtenidas son calculables en tiempo polinómico en el tamaño del modelo, por medio de la resolución de ciertos problemas de programación lineal definidos a partir de la matriz de incidencia de la red (en este sentido, las técnicas desarrolladas pueden considerarse estructurales). Las cotas calculadas dependen sólamente de los valores medios de las variables aleatorias que describen la temporización del sistema, y son independientes de los momentos de mayor orden. Esta independencia de la forma de las distribuciones de probabilidad asociadas puede considerarse como una útil generalización de otros resultados existentes para distribuciones particulares, puesto que los momentos de orden superior son, habitualmente, desconocidos en la realidad y difíciles de estimar. Finalmente, las técnicas desarrolladas se aplican al análisis de diferentes ejemplos tomados de la literatura sobre sistemas informáticos distribuidos y sistemas de fabricación. ******* Product form queueing networks have long been used for the performance evaluation of computer systems. Their success has been due to their capability of naturally expressing sharing of resources and queueing, that are typical situations of traditional computer systems, as well as to their efficient solution algorithms, of polynomial complexity on the size of the model. Unfortunately, the introduction of synchronization constraints usually destroys the product form solution, so that general concurrent and distributed systems are not easily studied with this class of models. Petri nets have been proved specially adequate to model parallel and distributed systems. Moreover, they have a well-founded theory of analysis that allows to investigate a great number of qualitative properties of the system. In the original definition, Petri nets did not include the notion of time, and tried to model only the logical behaviour of systems by describing the causal relations existing among events. This approach showed its power in the specification and analysis of concurrent systems in a way independent of the concept of time. Nevertheless the introduction of a timing specification is essential if we want to use this class of models for the performance evaluation of distributed systems. One of the main problems in the actual use of timed and stochastic Petri net models for the quantitative evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain, whose dimension is given by the size of the state space of the model. Structural computation of exact performance measures has been possible for some subclasses of nets such as those with state machine topology. These nets, under certain assumptions on the stochastic interpretation are isomorphic to Gordon and Newell's networks, in queueing theory terminology. In the general case, efficient methods for the derivation of performance measures are still needed. Two complementary approaches to the derivation of exact measures for the analysis of distributed systems are the utilization of approximation techniques and the computation of bounds. Approximate values for the performance parameters are in general more efficiently derived than the exact ones. On the other hand, "exactness" only exists in theory! In other words, numerical algorithms must be applied in practice for the computation of exact values, therefore making errors is inevitable. Performance bounds are useful in the preliminary phases of the design of a system, in which many parameters are not known accurately. Several alternatives for those parameters should be quickly evaluated, and rejected those that are clearly bad. Exact (and even approximate) solutions would be computationally very expensive. Bounds become useful in these instances since they usually require much less computation effort. The computation of upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is considered in this work. In particular, we study the throughput of transitions, defined as the average number of firings per time unit. For this measure we try to compute upper and lower bounds in polynomial time on the size of the net model, by means of proper linear programming problems defined from the incidence matrix of the net (in this sense, we develop structural techniques). These bounds depend only on the mean values and not on the higher moments of the probability distribution functions of the random variables that describe the timing of the system. The independence of the probability distributions can be viewed as a useful generalization of the performance results, since higher moments of the delays are usually unknown for real cases, and difficult to estimate and assess. From a different perspective, the obtained results can be applied to the analysis of queueing networks extended with some synchronization schemes. Monoclass queueing networks can be mapped on stochastic Petri nets. On the other hand, stochastic Petri nets can be interpreted as monoclass queueing networks augmented with synchronization primitives. Concerning the presentation of this manuscript, it should be mentioned that chapter 1 has been written with the object of giving the reader an outline of the stochastic Petri net model: its definition, terminology, basic properties, and related concepts, together with its deep relation with other classic stochastic network models. Chapter 2 is devoted to the presentation of the net subclasses considered in the rest of the work. The classification presented here is quite different from the one which is usual in the framework of Petri nets. The reason lies on the fact that our classification criterion, the computability of visit ratios for transitions, is introduced for the first time in the field of stochastic Petri nets in this work. The significance of that criterion is based on the important role that the visit ratios play in the computation of upper and lower bounds for the performance of the models. Nevertheless, classical important net subclasses are identified here in terms of the computability of their visit ratios from different parameters of the model. Chapter 3 is concerned with the computation of reachable upper and lower bounds for the most restrictive subclass of those presented in chapter 2: marked graphs. The explanation of this fact is easy to understand. The more simple is the model the more accessible will be the techniques an ideas for the development of good results. Chapter 4 provides a generalization for live and bounded free choice nets of the results presented in the previous chapter. Quality of obtained bounds is similar to that for strongly connected marked graphs: throughput lower bounds are reachable for bounded nets while upper bounds are reachable for 1-bounded nets. Chapter 5 considers the extension to other net subclasses, like mono-T-semiflow nets, FRT-nets, totally open deterministic systems of sequential processes, and persistent nets. The results are of diverse colours. For mono-T-semiflow nets and, therefore, for general FRT-nets, it is not possible (so far) to obtain reachable throughput bounds. On the other hand, for bounded ordinary persistent nets, tight throughput upper bounds are derived. Moreover, in the case of totally open deterministic systems of sequential processes the exact steady-state performance measures can be computed in polynomial time on the net size. In chapter 6 bounds for other interesting performance measures are derived from throughput bounds and from classical queueing theory laws. After that, we explore the introduction of more information from the probability distribution functions of service times in order to improve the bounds. In particular, for Coxian service delay of transitions it is possible to improve the throughput upper bounds of previous chapters which held for more general forms of distribution functions. This improvement shows to be specially fruitful for live and bounded free choice nets. Chapter 7 is devoted to case studies. Several examples taken from literature in the fields of distributed computing systems and manufacturing systems are modelled by means of stochastic Petri nets and evaluated using the techniques developed in previous chapters. Finally, some concluding remarks and considerations on possible extensions of the work are presented

    Time-optimal control of large-scale systems of systems using compositional optimization

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    Optimization of industrial processes such as manufacturing cells can have great impact on their performance. Finding optimal solutions to these large-scale systems is, however, a complex problem. They typically include multiple subsystems, and the search space generally grows exponentially with each subsystem. In previous work we proposed Compositional Optimization as a method to solve these type of problems. This integrates optimization with techniques from compositional supervisory control, dividing the optimization into separate sub-problems. The main purpose is to mitigate the state explosion problem, but a bonus is that the individual sub-problems can be solved using parallel computation, making the method even more scalable. This paper further improves on compositional optimization with a novel synchronization method, called partial time-weighted synchronization (PTWS), that is specifically designed for time-optimal control of asynchronous systems. The benefit is its ability to combine the behaviour of asynchronous subsystems without introducing additional states or transitions. The method also reduces the search space further by integrating an optimization heuristic that removes many non-optimal or redundant solutions already during synchronization. Results in this paper show that compositional optimization efficiently generates global optimal solutions to large-scale realistic optimization problems, too big to solve when based on traditional monolithic models. It is also shown that the introduction of PTWS drastically decreases the total search space of the optimization compared to previous work

    Petri net approaches for modeling, controlling, and validating flexible manufacturing systems

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    In this dissertation, we introduce the fundamental ideas and constructs of Petri net models such as ordinary, timed, colored, stochastic, control, and neural, and present some studies that emphasize Petri nets theories and applications as extended research fields that provide suitable platforms in modeling, controlling, validating, and evaluating concurrent systems, information systems, and a versatile dynamic system and manufacturing systems;We then suggest some of extensions that help make Petri nets useful for modeling and analyzing discrete event systems and manufacturing systems models based on the context of a versatile manufacturing system, and applies extended Petri nets models to several manufacturing systems such as an assembly cell, an Automated Palletized Conveyor System, and a tooling machine to show increased modeling power and efficient analysis methods;Finally, Validation methods are presented for these models and results of a performance analysis from a deterministic and stochastic model are used to reorganize and re-evaluate a manufacturing system in order to increase its flexibility
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