Resource Scheduling Scheme for Grid Computing and Its Petri Net Model and Analysis

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

In this chapter, modeling of GRNs using Petri net theory is considered. It aims at providing a conceptual understanding of Petri nets to enable the reader to explore GRNs applying Petri net modeling and analysis techniques. Starting with an overview on modeling biochemical networks using Petri nets, the state-of-the-art with focus on GRNs is described. Other modeling techniques, for example, hybrid Petri nets are discussed. Basic concepts of Petri net theory are introduced involving special analysis techniques for modeling biochemical systems, for example, MCT-sets, T-clusters, and Mauritius maps. To illustrate these Petri net concepts, a more complex case study–the gene regulation in Duchenne Muscular Dystrophy–is explained in detail, considering the biological background and the interpretation of analysis results. Considering both, advantages and disadvantages, the chapter demonstrates the usefulness of Petri net modeling, in particular for GRNs.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

Timed Petri nets (TPNs) have been widely used for modeling discrete-event systems of diverse manufacturing and service industries. In this article, we introduce a reachability tree-based optimization algorithm to optimize cyclic schedules of TPNs. In particular, we focus on a special class of cyclic schedules that are referred to as one-cyclic schedules, i.e., the algorithm efficiently finds the optimal one-cyclic transition firing schedule of a TPN. The proposed scheduling method can be robustly applied and extended to a number of different scheduling models since the methodology is not bounded to a specific domain. To enhance the computational performance, we establish a set of transition ordering constraints that can reduce the tree size during the search procedure. We evaluate the computational efficiency of the suggested algorithm by examining robotized manufacturing systems where one-cyclic schedules are popularly being used. It is numerically shown that the proposed algorithm is computationally more efficient than the previously studied Petri net-based optimization methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Resource scheduling is one of the most important managerial issues in diverse industrial systems. An optimal scheduling method for a certain industrial system is often locally developed by utilizing domain-specific operational properties. Although such domain-dependent knowledge can contribute to enhancing the computational efficiency of an optimization method, such an approach has a weak point that the method might not be applicable to scheduling problems of different industrial fields. Our motivation is to develop an algorithm for optimizing steady-state schedules that can be robustly applied for various types of discrete-event systems. The algorithm is developed on the basis of the Petri net modeling framework as it is widely being used for describing cyclic behaviors of diverse manufacturing systems, service systems, and social systems. It is experimentally shown that the proposed algorithm is computationally efficient compared with the existing cyclic scheduling methods.

This paper deals with the modeling and control of discrete event robotic manufacturing cells using Petri nets, and proposes a methodology of model based design and implementation of hierarchical and distributed control. Hierarchical Petri net models are adopted; conceptual Petri net model and detailed Petri net model. The overall detailed Petri net model is decomposed into local Petri net models which are used by the local machine controllers. The upper level station controller coordinates the distributed local controllers so that the aggregate behavior of decomposed subnets is the same as that of the original Petri net. The overall control system is implemented using multithreaded programming based on Petri net based multitask processing. Simulation experiments show that the distributed Petri net model based control system can perform the overall multitask processing control by coincidence of the behavior of the real system with the local Petri net models.

Modelling and analysis of kanban-controlled (just-in-time) production systems under realistic assumptions presents a number of challenges, including the ability to conduct both qualitative and quantitative analysis, and the ability to model control policies. These challenges are due, in part, to station interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modelling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modelling manufacturing systems. PNs are a graphical and mathematical technique useful for modelling concurrent, asynchronous, distributed, parallel, non-deterministic and stochastic systems. PN models can be analysed to determine both their qualitative and quantitative properties. In this paper, we develop stochastic, coloured PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible kanban system (FKS) policy. The resulting models can be used to represent JIT systems of arbitrary size, producing single or multiple types of products, with fixed order points 1. The models are shown to be live and bounded, and can be simulated to produce quantitative results. Sample simulation results are presented to illustrate the models' capabilities.

The explosive growth of the Internet of Things (IoT) has led to the emergence of the IoT-fog-cloud continuum, in an attempt to facilitate the real-time processing of IoT data. In such multi-tier environments, it is crucial to adopt an efficient resource allocation and scheduling scheme, in order to provide effective load balancing and timeliness for the real-time workload. A load balancing approach that has been proven to be efficient and effective in traditional distributed environments, is the power of two choices – or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex> choices, in its general form. Only recently has this technique been examined in multi-tier environments, without considering, however, important aspects of such frameworks. To this end, in this paper we propose and investigate three resource allocation and scheduling heuristics for real-time workflow jobs in an IoT-fog-cloud environment. The first strategy, performs exhaustive search at each scheduling step in order to find the most suitable resource in the fog and cloud layers for the workload assignment. On the other hand, the two other policies adopt the power of two choices approach. The simulation results shed light on interesting insights regarding the performance and applicability of each method.

Docker as the representative container technology promotes the rapid development of container cloud with its flexible, efficient and fast characteristics. As a better resource virtualization technology, container is widely recognized and favored by the industry. The resource scheduling strategy in the container cloud has an important impact on the cluster performance. The default priorities strategy of Kubernetes container orchestration tool only considers CPU and memory. With the complexity of the production environment, only considering the above two factors in the priorities stage can easily lead to some node load imbalance, which is difficult to guarantee the cluster service performance. In order to balance the resources of container clusters, this paper proposes a new priorities stage strategy based on Kubernetes' default scheduling strategy, which takes the storage and network bandwidth of task nodes into account, then calculates the weight of each resource, and finally puts it into the scoring formula as the basis of resource scheduling. By comparing the load balancing rate of the default priorities scheduling algorithm and the improved priorities scheduling algorithm, it is verified that the improved container cloud resource scheduling strategy can make the load of the task nodes in the cluster more balanced.

To simulate and debug or diagnose manufacturing systems is always challenging. This paper presents a hybrid PLC-controlled and PC Visual Basic (VB)-based Human-Machine Interface (HMI) platform based on Petri net (PN) theory for Manufacturing Systems. An augmented PN model was adopted to design and simulate the operational sequence of the Flexible Manufacturing System (FMS) at the National Kaohsiung First University of Science and Technology (NKFUST). With the simulated PN model, the control sequences were quickly translated into PLC programs. A PC-based HMI monitoring system based on the PN model was developed to provide an intuitive offline simulation and online diagnostic tools for the FMS. This hybrid system shows many of advantages by using the economical discrete control unit with PLC, and PC-based HMI using PN model as a base. The discrete event control sequence of an FMS can be easily modeled and evaluated before its build-up. More importantly, it can be diagnosed online when the system is malfunctioning. That is, the presented system provides an adequate means for offline system design, simulation, performance evaluation, and quick online system diagnostic.

&lt;p&gt;Cloud manufacturing is a grand manufacturing concept aimed at reducing the waste of manufacturing resources. By borrowing the ideas of cloud computing and utilizing information technology to achieve high sharing of manufacturing resources, the core issues that both the supply and demand sides are concerned about in the cloud manufacturing process are price, product quality, and product production cycle. Therefore, this paper constructs a manufacturing process resource scheduling model that includes three elements. In order to solve the optimal solution of the model, an improved intelligent algorithm is used to solve it. The intelligent algorithm is based on the advantages of the gray wolf algorithm in solving accuracy and convergence speed. The integration of the Bat algorithm in the gray wolf algorithm improves the search ability and performance of the original gray wolf algorithm. At the same time, the gray wolf algorithm can avoid the convergence speed of the Bat algorithm from changing with the increase of iteration times. The phenomenon of slow or almost stopping. To avoid generating local optimal solutions, the accuracy of the cloud resource scheduling model and algorithm solution constructed in this paper were verified through the construction of a simulation environment. &lt;/p&gt; &lt;p&gt;&amp;nbsp;&lt;/p&gt;

Based on the workflow management coalition (WFMC) standard and component software technologies, this paper addresses our Petri-nets-based approach for workflow and process automation. Petri nets provide graphical and mathematical formalisms for work-flow process definition and analysis. In this paper, we will present how to use Petri nets and a toolkit NCUPN (National Central University Petri Nets toolkit) for process definition and analysis. NCUPN is a Petri nets modeling and analysis toolkit developed to help software engineers in drawing and doing analysis. Once a workflow process is drawn using NCUPN, analysis can be done automatically. In this paper, we will demonstrate how to use NCUPN to analyze behavioral properties of workflow process, such as deadlock, liveness, safety, and starvation.

The accelerated development in peer‐to‐peer and Grid computing has positioned them as promising next‐generation computing platforms. They enable the creation of virtual enterprises for sharing resources distributed across the world. However, resource management, application development and usage models in these environments is a complex undertaking. This is due to the geographic distribution of resources that are owned by different organizations or peers. The resource owners of each of these resources have different usage or access policies and cost models, and varying loads and availability. In order to address complex resource management issues, we have proposed a computational economy framework for resource allocation and for regulating supply and demand in Grid computing environments. This framework provides mechanisms for optimizing resource provider and consumer objective functions through trading and brokering services. In a real world market, there exist various economic models for setting the price of services based on supply‐and‐demand and their value to the user. They include commodity market, posted price, tender and auction models. In this paper, we discuss the use of these models for interaction between Grid components to decide resource service value, and the necessary infrastructure to realize each model. In addition to usual services offered by Grid computing systems, we need an infrastructure to support interaction protocols, allocation mechanisms, currency, secure banking and enforcement services. We briefly discuss existing technologies that provide some of these services and show their usage in developing the Nimrod‐G grid resource broker. Furthermore, we demonstrate the effectiveness of some of the economic models in resource trading and scheduling using the Nimrod/G resource broker, with deadline and cost constrained scheduling for two different optimization strategies, on the World‐Wide Grid testbed that has resources distributed across five continents. Copyright © 2002 John Wiley &amp; Sons, Ltd.

In a 5G ultra-dense network, dynamic network topology and traffic patterns lead to excessive system overhead and complex radio resource conflicts. The cloud radio access network and the fog computing have the advantages of high computation capabilities and low transmission delays. Therefore, by taking full advantage of these two characteristics, this study proposes a novel radio resource coordination and scheduling scheme in an ultra-dense cloud-based small cell network. Interference among small cells (or remote radio heads) can be avoided by implementing centralized cooperative processing in the base band unit pool in advance. Resource sharing in coordination and transfer depend on fog computing to relieve the overloaded cloud processing platform and reduce transmission delays, thereby maximizing resource utilization and minimizing system overhead when the network topology and number of users change dynamically. The simulation shows that the proposed scheme can increase the system throughput by 20% compared with the clustering-based algorithm; it can also increase system throughput by 33% compared with the graph coloring algorithm, decrease the signaling overhead by about 50%, and improve network’s quality of service.

This paper presents an approach to perform Activity Based Costing (ABC) with Petri nets. ABC is a powerful methodology to calculate various of discrete event systems (e.g. production systems). Petri net models of discrete event systems are easy to create, comprehend, and to perform analysis, the mathematics behind Petri nets is also easy to grasp. This paper shows how ABC can be performed with Petri nets, so that various involved in a discrete event system can be easily measured with the help of the Petri net model. After a short introduction to ABC and Petri nets, this paper shows the approach which basically embeds various cost drivers as firing costs and firing times of transitions in a Petri net model. This work also presents a case study that is done with GPenSIM, a toolbox realized with this approach.

This paper presents a decentralized Petri net (PN) based wireless sensor node architecture (PN-WSNA) to construct a flexible and reconfigurable WSN for intelligent monitoring systems. PN is a graphic based discrete event dynamic system (DEDS) modeling approach, and it is advantageous for modeling the system with concurrent and asynchronous systems. Therefore, the PN is usually used to construct agent based intelligent monitoring systems. The PN-WSNA system consists of a PN-WSNA kernel program and a PN-WSNA management program. The PN-WSNA kernel program is developed as an agent that is installed in the sensor node, and it is responsible of receiving and decoding PN models, collecting sensor data from analog and digital channels, intercommunication between sensor nodes, PN model inference and decision. On the other hand, the PN-WSNA management program is executed on a remote host computer, and it is responsible of distance sensor node managements via routing tables. More specially, a user interface is provided for system managers to edit PN models in a graphic manner, and the PN models can be delivered to the corresponding sensor node online without physical visits. Therefore, the proposed PN-WSNA system not only performs a reconfigurable WSN architecture, but also provides an easy graphical PN edit environment for constructing intelligent agents. Such a system can be applied to the factory automation, intelligent diagnosis, climate monitoring, etc. Finally, a simple prototype system is constructed using the Zigbee BAT mote modules to verify the proposed PN-WSNA system.