Stochastic Discrete Event Research Articles

Design, simulation, and optimal control for the Fab 30 wafer fabrication facility

The paper introduces a methodology for the optimal control of stochastic discrete event dynamic systems (SDEDS). In this methodology, performance analysis (PA) techniques are used to design state observer of SDEDS. System identification, sensitivity analysis and predictive control techniques lead to an optimal control system design for SDEDS.

Convergence Rate of Ordinal Optimization for StochasticDiscrete Event Systems

It is shown that a global optimization algorithm using ordinal comparison converges to the good enough designs with a convergence rate faster than any polynomial of the total computing budget. The result is established in the context of one-dependent regenerative processes under the exponential stability condition of the underlying systems. A systematic approach is introduced to check the exponential stability condition by the stochastic Lyapunov function criterion. Examples arising in queueing theory are employed to illustrate the developed criterion.

An algorithmic model for invasive species: Application to Caulerpa taxifolia (Vahl) C. Agardh development in the North-Western Mediterranean Sea

The purpose of the study is to evaluate the propagation of the green alga of tropical origin Caulerpa taxifolia (Vahl) C. Agardh in the north-western Mediterranean sea—introduced in 1984—by means of an algorithmic computer model. In order to take into account spatial interactions and anthropic dispersion or activities such as eradication and introduction of specific predators, the model is based on a coupling of a geographical information system (GIS) with a stochastic discrete event simulation. Even if the model has to cope with incomplete data and sampling difficulties encountered in the hostile environment of the sea, interesting calibration and validation procedures have been achieved, including spectral analysis of spatial simulation results. At this stage, the model seems capable of achieving a certain level of prediction: local pattern of expansion, increase of C. taxifolia biomass and covered surfaces, and invasive behaviour towards existing communities.

On the Convergence of Global Rational Approximants forStochastic Discrete Event Systems

Difficulties often arise in analyzing stochastic discrete event systems due to the so-called ’’curse of dimensionality‘‘. A typical example is the computation of some integer-parameterized functions, where the integer parameter represents the system size or dimension. Rational approximation approach has been introduced to tackle this type of computational complexity. The underline idea is to develop rational approximants with increasing orders which converge to the values of the systems. Various examples demonstrated the effectiveness of the approach. In this paper we investigate the convergence and convergence rates of the rational approximants. First, a convergence rate of order O(1/\sqrt{n}) is obtained for the so-called Type-1 rational approximant sequence. Secondly, we establish conditions under which the sequence of[n/n] Type-2 rational approximants has a convergence rate of order O(n^{\alpha}e^{-\beta\sqrt{n}}).

Algebraic structure of some stochastic discrete event systems, with applications

Generalized semi-Markov processes (GSMPs) and stochastic Petri nets (SPNs) are generally regarded as performance models (as opposed to logical models) of discrete event systems. Here we take the view that GSMPs and SPNS are essentially automata (generators) driven by input sequences that determine the timing of events. This view combines the deterministic, logical aspects and the stochastic, timed aspects of the two models. We focus on two conditions, (M) and (CX) (which we previously developed to study monotonicity and convexity properties of GSMPs), and the antimatroid and lattice structure they imply for the language generated by a GSMP or SPN. We illustrate applications of these structural properties in the areas of derivative estimation, simulation variance reduction, parallel simulation, and optimal control.

Introduction—discrete event simulation

This special section deals with the simulation of complex systems, such as computer, communications, and manufacturing systems—specifically focusing on stochastic discrete event simulation. Such systems are typically (but not always) modeled by a network of queues, in which jobs compete for the system's resources. For example, in an on-line computer database system, the jobs would represent transactions, and the system's resources would include processors, disks, main memory, data locks, etc. Since job arrival patterns and resource requirements are unpredictable, such systems are inherently stochastic (random). As these systems increase in complexity, it becomes increasingly difficult to build analytically tractable performance models; thus simulation, because of its versatility, often becomes the only viable analysis technique. This issue contains articles which span a broad range of current topics in simulation, including Richard Fujimoto's article is a state-of-the-art survey on the execution of simulation models on parallel processors. Fujimoto describes why discrete event simulations have proven to be a difficult class of applications to parallelize. He then describes two basic parallelization approaches (conservative and optimistic), and recent experience with these approaches, including his own results in which significant speedups have been obtained on nontrivial problems using the optimistic “Time Warp” approach. He also provides a critique and assessment of the basic approaches to parallel simulation. The article by Sanjay Jain, Karon Barber and David Osterfeld describes a system for factory scheduling. The scheduling system obtains the status of the plant floor using the factory's real-time monitoring and control computer system. This information is fed into the scheduler which generates a new schedule, and sends it back to the factory control computer. The scheduler integrates a simulation model (which simulates backwards in time), and an expert system whose rules encode scheduling heuristics. The system is currently in use at a highly automated General Motors component production facility. Alexander Dupuy, Jed Schwartz, Yechiam Yemini and David Bacon's article describes NEST, a UNIX-based environment for prototyping, modeling, and simulating distributed systems. NEST has a graphical interface for building simulation models. In addition, users can program (or prototype) “node functions” that implement the system's control algorithms (e.g., routing protocols in a communications network). The node functions are linked into the simulation, allowing simulation (and debugging) of a system using its actual control logic. With only minor modification, the node functions can be decoupled from the simulation and used to build the actual system. The authors illustrate this combined use of prototyping and simulation using the RIP protocol, a simple routing protocol for IP (Internet Protocol) networks. The authors also describe other features of NEST, including its ability to dynamically reconfigure the simulation model during execution, which permits the study of how the system reacts to changing conditions, such as link failures. The article by Peter Glynn is concerned with sensitivity analysis of simulation output. He discusses a general-purpose method for using simulation to estimate the derivative of a performance measure, and provides explicit formulae for estimating derivatives for several broad classes of stochastic processes that typically arise in discrete event simulations. Pierre L'Ecuyer's article is a timely survey on pseudorandom number generation. As L'Ecuyer explains, this topic has recently received renewed attention for a variety of reasons, including the proliferation of generators on microcomputers, the need for portable generators, the requirement for generators with very long periods (as machines get faster), and the application of pseudorandom number generators to cryptology. L'Ecuyer examines several classes of generators, outlines their theoretical and empirical properties, and discusses implementation issues as well. The article by David Miller presents a case study illustrating the use of simulation modeling to analyze the performance of an IBM semiconductor manufacturing facility in Essex Junction, Vermont. Miller describes the relevant background and goals of the modeling study, the modeling approach, and model validation. He then describes the results of the simulation experiments, which included investigating a variety of line-loading and scheduling policies. Miller found that a lot-release policy that keeps a fixed amount of work-in-progress in the line could significantly reduce the lot turnaround time without reducing throughput, when compared to the policy that was in use in the facility. Miller then describes the specific changes, suggested by the modeling study, that were implemented in Essex Junction, and the corresponding improvement in the facility's efficiency.

On-Line Control of Discrete Event Systems: Some Extensions of Perturbation Analysis

Standard optimization problems for stochastic Discrete Event Dynamic Systems (DEDS) are limited by the unavailability of closed-form expressions for sensitivity information (gradients or finite differences). We address the problem of estimating on line gradients to be used in conjunction with parameterized control policies and standard optimization schemes. By exploiting the flexibility provided by different sample path representations of the same underlying DEDS, we show that Perturbation Analysis techniques can be extended to more complicated queueing models than those analyzed thus far.