Admission control in stochastic event graphs

We first show that the expectation of convex increasing functions of the workload (or waiting time) in (max, +) linear systems, under a single input sequence, is multi-modular. This is done using a coupling argument and a vectorial version of Lindley's equation. Next, we use this result and the optimization theory based on multi-modular costs to construct the optimal open-loop admission control in general (max, +) linear systems under admission rate constraints. This optimization result only requires stationarity assumptions on the arrival process and on the service times of the servers in the system     

Asymptotic properties of stochastic timed event graphs

This paper addresses the asymptotic properties of stochastic timed event graphs. The transition firing times are random variables with general distribution. Asymptotic properties with respect to the net structure, the transition firing times and the initial marking are established on the basis of some new performance bounds. Applications to manufacturing systems are presented. We prove in particular a conjecture which claims that the throughput rate of a transfer line decreases to a positive value when the number of machines increases.     

Marking optimization of stochastic timed event graphs using IPA

This paper addresses the marking optimization of stochastic timed event graphs, where the transition firing times are generated by random variables with general distributions. The marking optimization problem consists of obtaining a given cycle time while minimizing a p-invariant criterion. We propose two heuristic algorithms, both starting from the optimal solution to the associated deterministic problem and iteratively adding tokens to adequate places as long as the given cycle time is not obtained. Infinitesimal perturbation analysis of the average cycle time with respect to the transition firing times is used to identify the appropriate places in which new tokens are added at each iteration. Numerical results show that the heuristic algorithms provide solutions better than the ones obtained by the existing methods.     

Analytic evaluation of the cycle time on networked conflicting timed event graphs in the (Max,+) algebra

This work deals with performance evaluation of Conflicting Timed Event Graph (CTEG), a class of Petri net exhibiting phenomena such as synchronization, parallelism and resources sharing. It is well known that the dynamic of Timed Event Graphs (TEG) admits a linear state space representation in the (Max,+) algebra which makes the analysis and control of this class easier. There is also a possibility of associating conflicts with the TEGs by adding conflict places that are mostly considered as safe; this extended class is called CTEG. We first present an analytic evaluation of the cycle time of CTEG as a function of the cycle time of each TEG and of the timers of the conflict places. Finally, in a more general context, we look for a relaxation of the safety hypothesis on the conflict places in order to model and evaluate the cycle time on CTEGs with multiple shared resources.     

非线性DEDS的周期时间配置与凝着色图

对于用极大极小函数描述的非线性离散事件动态系统(DEDS)，提出一种凝着色图方法。用该方法证明了不同周期时间的数日等于凝点的数日。在此基础上给出了能用状态反馈(独立)配置周期时间的充要条件，解决了与传统线性控制系统极点配置问题完全对应的问题。将该结果应用于线性DEDS，得到了配置域及缩短的周期时间。     

Cycle bases of graphs and sampled manifolds

Point samples of a surface in are the dominant output of a multitude of 3D scanning devices. The usefulness of these devices rests on being able to extract properties of the surface from the sample. We show that, under certain sampling conditions, the minimum cycle basis of a nearest neighbor graph of the sample encodes topological information about the surface and yields bases for the trivial and non-trivial loops of the surface. We validate our results by experiments.     

Model predictive control of P-time event graphs

This paper deals with model predictive control of discrete event systems modelled by P-time event graphs. First, the model is obtained by using the dater evolution model written in the standard algebra. Then, for the control law, we used the finite-horizon model predictive control. For the closed-loop control, we used the infinite-horizon model predictive control (IH-MPC). The latter is an approach that calculates static feedback gains which allows the stability of the closed-loop system while respecting the constraints on the control vector. The problem of IH-MPC is formulated as a linear convex programming subject to a linear matrix inequality problem. Finally, the proposed methodology is applied to a transportation system.     

Optimisation of invariant criteria for event graphs

The problem of obtaining a cycle time that is smaller than a given value in a strongly connected event graph, while minimizing an invariant linear criterion, is addressed. This linear criterion is based on a p-invariant of the strongly connected event graph under consideration. Some properties of the optimal solution are proved, and a heuristic algorithm and an exact algorithm which make it possible to reach a solution to the problem are given. Applications of the results to the evaluation of job shops and Kanban systems are proposed     

Detectability in stochastic discrete event systems

A discrete event system possesses the property of detectability if it allows an observer to perfectly estimate the current state of the system after a finite number of observed symbols, i.e., detectability captures the ability of an observer to eventually perfectly estimate the system state. In this paper we analyze detectability in stochastic discrete event systems (SDES) that can be modeled as probabilistic finite automata. More specifically, we define the notion of A-detectability, which characterizes our ability to estimate the current state of a given SDES with increasing certainty as we observe more output symbols. The notion of A-detectability is differentiated from previous notions for detectability in SDES because it takes into account the probability of problematic observation sequences (that do not allow us to perfectly deduce the system state), whereas previous notions for detectability in SDES considered each observation sequence that can be generated by the underlying system. We discuss observer-based techniques that can be used to verify A-detectability, and provide associated necessary and sufficient conditions. We also prove that A-detectability is a PSPACE-hard problem.     

Information-efficient control of discrete event stochastic systems

A state of a discrete event stochastic system (DESS) can be represented by a tuple of time-varying discrete parameters. The authors have extended the theory of controlled discrete event systems developed by Ramadge, Wonham and other researchers to stochastic modeling and performance measurement. This work presents some important characteristics of the DESS model. The problem of making the most efficient use of information-processing resources (sensors, computer capacity, etc.) in a special class of controlled systems is stated in a new, two-stage format. The format is used to develop a heuristic solution procedure of the problem. Finally, we perform a brief discussion of the model applicability to real-life design of automatic supervisors     

Disease management research using event graphs.

Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate abstraction level, also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course.     

Approximate throughput computation of stochastic marked graphs

A general iterative technique for approximate throughput computation of stochastic strongly connected marked graphs is presented. It generalizes a previous technique based on net decomposition through a single input-single output cut, allowing the split of the model through any cut. The approach has two basic foundations. First, a deep understanding of the qualitative behavior of marked graphs leads to a general decomposition technique. Second, after the decomposition phase, an iterative response time approximation method is applied for the computation of the throughput. Experimental results on several examples generally have an error of less than 3%. The state space is usually reduced by more than one order of magnitude; therefore, the analysis of otherwise intractable systems is possible     

用分层事件关系图实现系统仿真与分析*

现有的建模语言如UML、有穷状态自动机、Petri网、DEVS等不能完全满足工业中对时间系统建模的要求,企业常须自行开发建模语言和工具,或人为加工和抽象时间系统的设计以适应已有建模手段。使用事件关系图实现分层设计可以在一定程度上解决这一问题。该方法既方便了对复杂时间系统的设计,也使自动化仿真、分析和代码生成变得简易可行。     

Supervisory control of timed event graphs with partial specifications

This paper studies realizable firing time sequences under supervisory control in the max-algebra model of timed event graphs. A specification is assumed to be defined on firing times of a specified subset of transitions. Such a specification is called a partial specification. A necessary and sufficient condition for a partial specification to be realizable is presented under the assumption that all controllable transitions are in the specified subset. For a not realizable partial specification, the extremal realizable sequences are obtained as its approximations.     

Detecting logic errors in discrete-event simulation: reverse engineering through event graphs

Several inherent constraints remain in the model development process, even though modern enhancements to simulation environments have provided tools for code generation, debugging, and tracing. To develop a simulation model, the simulation analyst still needs to have expertise in a number of different fields, e.g., probability, statistics, design of experiments, modeling, systems engineering, software engineering, and computer programming. Although several simulation packages implement syntactic-checks and semantic-consistency-checks, typically, the simulation analyst needs to possess output-analysis-knowledge specifically aimed at verifying and checking the simulation code.Reverse engineering a graphical model, e.g., an event graph, from general purpose simulation code demonstrates an enhancement to the model development process. A reverse engineering step allows an analyst to check, both, the static and dynamic properties of the coded simulation model. Even though the reverse engineering produces an event-oriented view, the enhanced model development process provides a systematic approach for conversion from other world views. Overall, this enhanced process provides a framework which yields better analysis techniques.Better diagnostic assistance is achieved when viewing a combination of static and dynamic properties of the simulation code. Now, the analyst is able to find logical/execution errors, e.g., errors related to resource deadlocks, before running simulation experiments. Since the graphical model is generated from the simulation code, and the process combines views, the analyst also has a better framework for verifying the coded simulation model. Also, the reverse engineering step provides a structural model useful in converting between different simulation languages or systems. Improvements to the techniques for conversion between languages will facilitate reuse of existing programmed models.     

Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem

We present a dynamic programming based solution to a probabilistic reach-avoid problem for a controlled discrete time stochastic hybrid system. We address two distinct interpretations of the reach-avoid problem via stochastic optimal control. In the first case, a sum-multiplicative cost function is introduced along with a corresponding dynamic recursion which quantifies the probability of hitting a target set at some point during a finite time horizon, while avoiding an unsafe set during each time step preceding the target hitting time. In the second case, we introduce a multiplicative cost function and a dynamic recursion which quantifies the probability of hitting a target set at the terminal time, while avoiding an unsafe set during the preceding time steps. In each case, optimal reach while avoid control policies are derived as the solution to an optimal control problem via dynamic programming. Computational examples motivated by two practical problems in the management of fisheries and finance are provided.     

Interval analysis and dioid: application to robust controller design for timed event graphs

This paper deals with feedback controller synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a robust controller set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each controller is computed in order to guarantee that the closed-loop system behavior is greater than the lower bound of a reference model set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.     

Control of stochastic discrete event systems modeled byprobabilistic languages

In Garg et al. (1999) and Garg (1992) the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems (DESs) was introduced. In this paper, we study their supervisory control where the control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events, and increasing the occurrence probabilities of enabled events proportionately. This is a special case of “probabilistic supervision” introduced in Lawford and Wonham (1993). The control objective is to design a supervisor such that the controlled system never executes any illegal traces (their occurrence probability is zero), and legal traces occur with minimum prespecified occurrence probabilities. In other words, the probabilistic language of the controlled system lies within a prespecified range, where the upper bound is a “nonprobabilistic language” representing a legality constraint. We provide a condition for the existence of a supervisor. We also present an algorithm to test this existence condition when the probabilistic languages are regular (so that they admit probabilistic automata representation with finitely many states). Next, we give a technique to compute a maximally permissive supervisor online