Discrete Event Dynamic Systems Research Articles

Mapping Petri Nets onto a Calculus of Context-Aware Ambients

Petri nets are a graphical notation for describing a class of discrete event dynamic systems whose behaviours are characterised by concurrency, synchronisation, mutual exclusion and conflict. They have been used over the years for the modelling of various distributed systems applications. With the advent of pervasive systems and the Internet of Things, the Calculus of Context-aware Ambients (CCA) has emerged as a suitable formal notation for analysing the behaviours of these systems. In this paper, we are interested in comparing the expressive power of Petri nets to that of CCA. That is, can the class of systems represented by Petri nets be modelled in CCA? To answer this question, an algorithm is proposed that maps any Petri net onto a CCA process. We prove that a Petri net and its corresponding CCA process are behavioural equivalent. It follows that CCA is at least as expressive as Petri nets, i.e., any system that can be specified in Petri nets can also be specified in CCA. Moreover, tools developed for CCA can also be used to analyse the behaviours of Petri nets.

Novel Simulation Optimization Approach for Supply Chain Coordination and Management

The importance of supply chain management is paramount nowadays and this research seeks ways for better supply chain coordination. We present a roadmap for implementing true digital replicas of physical supply chains based on a disruptive simulation modeling approach. These digital replicas can enable the comparative evaluation of existing Just-In-Time (JIT) control policies for the first time without the unrealistic assumptions of existing studies in the literature. These realistic supply chain simulation models have the prospect of giving us better understanding of their behavior and of their complex dynamics. We provide guidelines for using the digital replicas and advanced optimization approaches to derive novel supply chain coordination policies pushing the field of JIT control beyond the state-of-the-art. An equally important contribution of this research is that it advances the field of hybrid discrete event-system dynamics (DES-SD) simulation with the prospect of pushing Systems Engineering to the next level. This research discusses theoretical foundations for mixing DES with SD simulation, and explores technical aspects and implementation details. The implications of this extent well beyond the supply chain field since both DES and SD have dozens of application areas including manufacturing, service systems and economics, social sciences, respectively. The paper is concluded with a discussion on the potential impact of the proposed approach including insights for practitioners, applicability of scientific results in industry and prerequisites for business process re-engineering.

An efficient simulation procedure for the expected opportunity cost using metamodels

Many decision problems in modern industries involve the performance optimization of discrete-event dynamic systems. Because of the stochasticity of these systems, performance usually is evaluated through simulation. Finding the optimal designs of these systems can be modeled as a ranking and selection problem. This research considers the problem of selecting the best design from among numerous designs. We minimized the expected opportunity cost (EOC) of incorrect selection with a limited computing budget. The entire domain of designs could be divided into several adjacent partitions, and the performances of designs in each partition were estimated using a regression metamodel. We assumed the underlying function in each partition to be quadratic. Using large deviations theory, we then derived an asymptotically optimal budget allocation rule and developed a sequential allocation algorithm to implement the allocation rule. The EOC measure was compared with the probability of correct selection measure in a set of large-scale simulation optimization problems. Numerical experiments verified the effectiveness of our proposed simulation procedure.

Identification of unobservable behavior in stochastic discrete event systems with a low number of sensors

Dynamic discrete event systems (DDES) are systems that evolve from the asynchronous occurrence of discrete events. Their versatility has become a critical modeling tool in different applications. Finding models that define the behavior of DES is a topic that has been addressed from different approaches, depending on the type of system to be modeled and the model's objective. This article focuses on the identification of timed models for stochastic discrete event systems. The identified model includes both observable and unobservable behavior. The objective of the method is achieved through the following steps:•Identifying the sequences of events observed at different time instances during the closed-loop operation of the system (observed language),•Inferring the stochastic behavior of time between events and modeling the observable behavior as a stochastic timed Interpreted Petri Net (st-IPN),•and finally, inferring the non-observable behavior using the language projection operation between the observed language and the language generated by the st-IPN.This method has novel aspects because it uses timed events, can be applied to systems with a low number of sensors and can infer unobservable behavior for any sequence of events.

Convergence rate analysis for optimal computing budget allocation algorithms

Ordinal optimization (OO) is a widely-studied technique for optimizing discrete-event dynamic systems (DEDS). It evaluates the performance of the system designs in a finite set by sampling and aims to correctly make ordinal comparison of the designs. A well-known method in OO is the optimal computing budget allocation (OCBA). It builds the optimality conditions for the number of samples allocated to each design, and the sample allocation that satisfies the optimality conditions is shown to asymptotically maximize the probability of correct selection for the best design. In this paper, we investigate two popular OCBA algorithms. With known variances for samples of each design, we characterize their convergence rates with respect to different performance measures. We first demonstrate that the two OCBA algorithms achieve the optimal convergence rate under measures of probability of correct selection and expected opportunity cost. It fills the void of convergence analysis for OCBA algorithms. Next, we extend our analysis to the measure of cumulative regret, a main measure studied in the field of machine learning. We show that with minor modification, the two OCBA algorithms can reach the optimal convergence rate under cumulative regret. It indicates the potential of broader use of algorithms designed based on the OCBA optimality conditions.

Control laws synthesis for timed event graphs subject to generalised marking constraints by Min-Plus algebra: application to cluster tools

This paper discusses the problem of control laws for Discrete Event Dynamic Systems (DEDSs) represented by Timed Event Graphs (TEGs) under Generalized Marking Constraints (GMCs). The behaviour of TEGs is described using linear equations while GMCs are expressed by weighted inequalities in Min-Plus algebra. We formulate the problem in terms of control linear Min-Plus models. Hence, an algebraic method to calculate control laws ensuring the respect of GMCs is suggested. And once sufficient conditions are satisfied, we propose casual feedbacks to guarantee these marking specifications. Besides, the proposed control strategy is applied to a dual-armed cluster tool, a well-known industrial application.

Asymptotic optimality of myopic ranking and selection procedures

Ranking and selection (R&S) is a popular model for studying discrete-event dynamic systems. It aims to select the best design (the design with the largest mean performance) from a finite set, where the mean of each design is unknown and has to be learned by samples. Great research efforts have been devoted to this problem in the literature for developing procedures with superior empirical performance and showing their optimality. In these efforts, myopic procedures were popular. They select the best design using a “naive” mechanism of iteratively and myopically improving an approximation of the objective measure. Although they are based on simple heuristics and lack theoretical support, they turned out highly effective, and often achieved competitive empirical performance compared to procedures that were proposed later and shown to be asymptotically optimal. In this paper, we theoretically analyze these myopic procedures and prove that they also satisfy the optimality conditions of R&S, just like some other popular R&S methods. It explains the good performance of myopic procedures in various numerical tests, and provides good insight into the structure and theoretical development of efficient R&S procedures.

Survey on applications of algebraic state space theory of logical systems to finite state machines

Algebraic state space theory (ASST) of logical systems, developed based on the semi-tensor product (STP) which is a new matrix analysis tool built in recent ten years, provides an algebraic analysis approach for many fields of science, such as logical dynamical systems, finite-valued systems, discrete event dynamic systems, and networked game systems. This study focuses on comprehensively surveying the applications of the ASST method to the field of finite state machines (FSMs). Some necessary preliminaries on the method are first reviewed. Then the applications of the method in the FSM field are reviewed, including deterministic FSMs, nondeterministic FSMs, probabilistic FSMs, networked FSMs, and controlled and combined FSMs. In addition, other applications related to both STP and FSMs are surveyed, such as the application of FSM to Boolean control networks and the application of graph theory to FSMs. Finally, some potential research directions with respect to the ASST method in the FSM field are predicted.

On multi-scale event-based optimization

For most practical discrete event dynamic systems (DEDSs), the system structures are hierarchical and contain multiple subsystems, which leads to the fact that state transitions within different scales are differentiated. Directly applying standard Markov decision process (MDP) or event-based optimization (EBO) methods to model and optimize such problems is inefficient and often encounter issues like the curse of dimensionality. In this paper, a multi-scale event-driven optimization (MEBO) method is proposed. To accurately capture system state transitions at different scales, MEBO defines macro and micro events, respectively. With proper definition, the size of event space can be constant or grows only linearly with the problem size. Furthermore, two policy iteration algorithms are proposed to solve MEBO problems and the local optimality of the algorithms is proved theoretically. an example based on queueing system. Finally, the effectiveness of the MEBO methods are demonstrated by an example of admission control in queuing system. It is hoped that this method can be used as a supplement to EBO method and provide a new perspective for performance optimization of multi-scale DEDSs.

Characterizations and Optimization for Resilient Manufacturing Systems With Considerations of Process Uncertainties

Abstract The recent COVID-19 pandemic reveals the vulnerability of global supply chains: the unforeseen supply crunches and unpredictable variability in customer demands lead to catastrophic disruption to production planning and management, causing wild swings in productivity for most manufacturing systems. Therefore, a smart and resilient manufacturing system (S&RMS) is promised to withstand such unexpected perturbations and adjust promptly to mitigate their impacts on the system’s stability. However, modeling the system’s resilience to the impacts of disruptive events has not been fully addressed. We investigate a generalized polynomial chaos (gPC) expansion-based discrete-event dynamic system (DEDS) model to capture uncertainties and irregularly disruptive events for manufacturing systems. The analytic approach allows a real-time optimization for production planning to mitigate the impacts of intermittent disruptive events (e.g., supply shortages) and enhance the system’s resilience. The case study on a hybrid bearing manufacturing workshop suggests that the proposed approach allows a timely intervention in production planning to significantly reduce the downtime (around one-fifth of the downtime compared to the one without controls) while guaranteeing maximum productivity under the system perturbations and uncertainties.

Modeling and Optimizing Based on OTCPN in Multi-Tier Shuttle Warehousing System

This paper models the multi-tier shuttle warehousing system and optimizes the system structure and control strategy. This kind of system is a discrete event dynamic system because it only takes place at discrete time points, while previous warehousing system models. We propose the object-oriented timed colored Petri net to model it, to improve the accuracy of the model and avoid the problem of status explosion in the process of Petri net modeling. We propose two control strategy optimization methods: one is to balance the task assignment, and the other is to change the return time point of the buffer status information. The results of numerical experiments show that consideration of both optimization strategies can reduce the total picking time by 40 % ∼ 62 % . Additionally, we analyze the influence of the buffer capacity. The results show that the buffer capacity can reduce the total picking time, and enough amount of buffer capacity has the same effect as control strategy optimization.

Compensating for part arrival uncertainties in two-processing-machine, one-buffer flow lines: Inventory flexibility design based on the system transient performances

• A structured Markov process model for the proposed flow lines;. • Transition equation derivation for the flow lines;. • The algorithms for factoring a class of states to derive closed-form expressions;. • System transient performance analysis of the flow lines system;. • Discrete event dynamic system simulation and verification. In one-of-a-kind production (OKP), a flow line with two distinct deterministic processing time machines and one “flexible” storage buffer is studied from the perspective of manufacturing system design and transient behaviour analysis. This manufacturing process is disrupted by part arrival uncertainties and is considered a discrete dynamic stochastic system. The dynamic behaviour of the flow line is structured as a transfer line with multi-state machines and finite-storage buffers by a discrete-time, discrete-state Markov chain for the transient performance analysis, optimal design and efficient production operation. To assess the dynamic disruptions and further limit the cascading effects on the flow line, in the presented analytical model, the studies quantify the evolution of a basic serial production process over time; and meanwhile, we evaluate and optimize the manufacturing system transient performance to determine the optimal design of inventory flexibility as a function of the time and states. By factoring out a class of appropriate transient states associated with an initial state at a certain time slot and deriving closed-form expressions using the transition equations, we sought to determine the transient probabilities of the manufacturing system states to establish relationships between the variable system parameters and the performance measures. By embedding these practical results with quantitative precision in an optimal design process of inventory flexibility, we consider setting the storage buffer level between two processing machines for refined production optimization and control when the part arrival uncertainties and lack of synchronization constantly occur in this serial manufacturing system.

Stochastic modelling and evaluation using GreatSPN

GreatSPN is a tool that supports model-based (stochastic) analysis of Discrete Event Dynamic Systems (DEDS) modeled as Generalized Stochastic Petri Nets or one of its extensions like StochasticWell-formed Nets, Deterministic and Stochastic Petri Nets among the other. Performance evaluation of the timed and stochastic properties of the modeled systems was the initial reason for the tool development, and it is today a large and flexible framework that incorporates several analysis techniques, performance index types, variegated transition timing specifications, etc. In this paper we report the current status of the GreatSPN framework, with a focus on the modularity, the types of stochastic analysis, the specification and evaluation functionalities, and its role for the performance evaluation.

Optimization and Simulation of Accounting Information Practice Model Assisted by Discrete Dynamic Events

The performance function expressed by the expected value of the discrete event dynamic system usually does not have a closed analytical expression, so it can only be estimated by the Monte-Carlo method. The inherent limitations of the Monte-Carlo method (low simulation efficiency) and the complexity of the system bring a lot to the simulation optimization problem. A huge challenge has come. A reasonable combination of mathematical methods and computer simulation technology is an important direction to study the optimal design of DESD. On the basis of linear systems on maximal algebras, this article studies a class of multimodel systems on maximal algebras. This article presents a non-Markov DEDS time-synchronized parallel simulation algorithm and proves that the common random number method can maximize the simulation efficiency of an existing event-synchronized algorithm. We take advantage of the inherent parallelism of genetic algorithm, and combine the idea of parallel simulation and DEDS order optimization to give an optimization algorithm for discrete parameter space DEDS. This article discusses the relationship between ultimate control, internal control, and accounting information quality. This article analyzes the relationship between ultimate control right, internal control, and accounting information quality. We use the manipulated accruals calculated by the modified Jones model and the earnings response coefficient of the earnings-return model to measure the quality of accounting information, and analyze the impact of the ultimate control ratio and internal control level on the quality of accounting information. Based on the difference in the nature of the controller and the ratio of ultimate control rights, this article examines the difference in the effect of internal control on the quality of accounting information in companies with high and low ratios of ultimate control rights. The robustness tests of the two accounting information measurement models are carried out, respectively, and the results obtained are basically consistent with the empirical research conclusions. The situation is the most important to its own development. Among them, the asset turnover rate has a greater effect on the early warning of corporate financial crisis, and the status of the current asset turnover rate and the total asset turnover rate in the financial early warning is also crucial. This article studies the correlation between the overall level of internal control and the quality of accounting information, avoiding the one-sidedness caused by using a single index to measure the level of internal control.

Max-plus steady states in discrete event dynamic systems with inexact data

Max-plus steady states in discrete event dynamic systems with inexact data

Uncertainty on Discrete-Event System Simulation

Uncertainty Propagation methods are well-established when used in modeling and simulation formalisms like differential equations. Nevertheless, until now there are no methods for Discrete-Dynamic Systems. Uncertainty-Aware Discrete-Event System Specification (UA-DEVS) is a formalism for modeling Discrete-Event Dynamic Systems that include uncertainty quantification in messages, states, and event times. UA-DEVS models provide a theoretical framework to describe the models’ uncertainty and their properties. As UA-DEVS models can include continuous variables and non-computable functions, their simulation could be non-computable. For this reason, we also introduce Interval-Approximated Discrete-Event System Specification (IA-DEVS), a formalism that approximates UA-DEVS models using a set of order and bounding functions to obtain a computable model. The computable model approximation produces a tree of all trajectories that can be traversed from the original model and some erroneous ones introduced by the approximation process. We also introduce abstract simulation algorithms for IA-DEVS, present a case study of UA-DEVS, its IA-DEVS approximation and, its simulation results using the algorithms defined.

Petri Net-Based Semi-Compiled Code Generation for Programmable Logic Controllers

Industrial discrete event dynamic systems (DEDSs) are commonly modeled by means of Petri nets (PNs). PNs have the capability to model behaviors such as concurrency, synchronization, and resource sharing, compared to a step transition function chart or GRAphe Fonctionnel de Commande Etape Transition (GRAFCET) which is a particular case of a PN. However, there is not an effective systematic way to implement a PN in a programmable logic controller (PLC), and so the implementation of such a controller outside a PLC in some external software that will communicate with the PLC is very common. There have been some attempts to implement PNs within a PLC, but they are dependent on how the logic of places and transitions is programmed for each application. This work proposes a novel application-independent and platform-independent PN implementation methodology. This methodology is a systematic way to implement a PN controller within industrial PLCs. A great portion of the code will be validated automatically prior to PLC implementation. Net structure and marking evolution will be checked on the basis of PN model structural analysis, and only net interpretation will be manually coded and error-prone. Thus, this methodology represents a systematic and semi-compiled PN implementation method. A use case supported by a digital twin (DT) is shown where the automated solution required by a manufacturing system is carried out and executed in two different devices for portability testing, and the scan cycle periods are compared for both approaches.

Multi-paradigm modelling for cyber\u2013physical systems: a descriptive framework

The complexity of cyber–physical systems (CPSs) is commonly addressed through complex workflows, involving models in a plethora of different formalisms, each with their own methods, techniques, and tools. Some workflow patterns, combined with particular types of formalisms and operations on models in these formalisms, are used successfully in engineering practice. To identify and reuse them, we refer to these combinations of workflow and formalism patterns as modelling paradigms. This paper proposes a unifying (Descriptive) Framework to describe these paradigms, as well as their combinations. This work is set in the context of Multi-Paradigm Modelling (MPM), which is based on the principle to model every part and aspect of a system explicitly, at the most appropriate level(s) of abstraction, using the most appropriate modelling formalism(s) and workflows. The purpose of the Descriptive Framework presented in this paper is to serve as a basis to reason about these formalisms, workflows, and their combinations. One crucial part of the framework is the ability to capture the structural essence of a paradigm through the concept of a paradigmatic structure. This is illustrated informally by means of two example paradigms commonly used in CPS: Discrete Event Dynamic Systems and Synchronous Data Flow. The presented framework also identifies the need to establish whether a paradigm candidate follows, or qualifies as, a (given) paradigm. To illustrate the ability of the framework to support combining paradigms, the paper shows examples of both workflow and formalism combinations. The presented framework is intended as a basis for characterisation and classification of paradigms, as a starting point for a rigorous formalisation of the framework (allowing formal analyses), and as a foundation for MPM tool development.

Buffer allocation design for unreliable production lines using genetic algorithm and finite perturbation analysis

The buffer allocation problem in production lines is an NP-hard combinatorial optimisation problem. This paper proposes a new hybrid optimisation approach (using simulation) relying on genetic algorithm (GA) and finite perturbation analysis (FPA). Unlike the infinitesimal perturbation analysis, which deals with small (infinitesimal variation) perturbations for estimating gradients of the performance measure, FPA deals with larger (finite) or more lasting perturbations. It is an extension specifically dedicated to discrete decision variables and applicable to most discrete-event dynamic systems. The proposed method allows a global search using GA, with refinement in specific solution-space regions using FPA. The main objective is to maximise the average production rate of a production line with unreliable machines, by allocating the total buffer capacity in locations between machines. Extensive numerical experiments show that: (1) the proposed hybrid GA-FPA method clearly outperforms the state-of-the-art methods from the literature; (2) combining FPA and GA is beneficial when compared to employing GA or FPA independently.

Simulation Model to Determine Ratios between Quay, Yard and Intra-Terminal Transfer Equipment in an Integrated Container Handling System

This paper presents a generic simulation model to determine the equipment mix (quay, yard and intra-terminal transfer) for a Container Terminal Logistics Operations System (CTLOS). The simulation model for the CTLOS, a typical type of discrete event dynamic system (DEDS), consists of three sub-models: ship queue, loading-unloading operations and yard-gate operations. The simulation model is empirically applied to phase 1 of the Yangshan Deep Water Port in Shanghai. This study considers different scenarios in terms of container throughput levels, equipment utilization rates, and operational bottlenecks, and presents a sensitivity analysis to evaluate and choose reasonable equipment ratio ranges under different operational conditions.