Kriging metamodeling for simulation

Many scientific disciplines use mathematical models to describe complicated real systems. Often, analytical methods are inadequate, so simulation is applied. This thesis focuses on computer intensive simulation experiments in Operations Research/Management Science. For such experiments it is necessary to apply interpolation. In this thesis, Kriging interpolation for random simulation is proposed and a novel type of Kriging - called Detrended Kriging - is developed. Kriging turns out to give better predictions in random simulation than classic low-order polynomial regression. Kriging is not sensitive to variance heterogeneity: i.e. Kriging is a robust method. Moreover, the thesis develops a novel method to select experimental designs for expensive simulation. This method is sequential, and accounts for the specific input/output function implied by the underlying simulation model. For deterministic simulation the designs are constructed through cross-validation and jackknifing, whereas for random simulation the customization is achieved through bootstrapping. The novel method simulates relatively more input combinations in the interesting parts of the input/output function, and gives better predictions than traditional Latin Hypercube Sample designs with prefixed sample sizes.

Analysing stochastic call demand with time varying parameters

In spite of increasingly sophisticated workforce management tools, a significant gap remains between the goal of effective staffing and the present difficulty predicting the stochastic demand of inbound calls. We have investigated the hypothesized nonhomogeneous Poisson process model of modem pool callers of the University community. In our case, we tested if the arrivals could be approximated by a piecewise constant rate over short intervals. For each of 1 and 10-minute intervals, based on the close relationship between the Poisson process and the exponential distribution, the test results did not show any sign of homogeneous Poisson process. We have examined the hypothesis of a nonhomogeneous Poisson process by a transformed statistic. Quantitative and graphical goodness-of-fit tests have confirmed nonhomogeneous Poisson process. Further analysis on the intensity function revealed that linear rate intensity was woefully inadequate in predicting time varying arrivals. For sinusoidal rate model, difficulty arose in setting the period parameter. Spline models, as an alternative to parametric modelling, had more control of balance between data fitting and smoothness, which was appealing to our analysis on call arrival process

Design of Experiments: An Overview

Design Of Experiments (DOE) is needed for experiments with real-life systems, and with either deterministic or random simulation models. This contribution discusses the different types of DOE for these three domains, but focusses on random simulation. DOE may have two goals: sensitivity analysis including factor screening and optimization. This contribution starts with classic DOE including 2k-p and Central Composite designs. Next, it discusses factor screening through Sequential Bifurcation. Then it discusses Kriging including Latin Hyper cube Sampling and sequential designs. It ends with optimization through Generalized Response Surface Methodology and Kriging combined with Mathematical Programming, including Taguchian robust optimization.simulation;sensitivity analysis;optimization;factor screening;Kriging;RSM;Taguchi

Experimental Design for Sensitivity Analysis, Optimization and Validation of Simulation Models

This chapter gives a survey on the use of statistical designs for what-if analysis in simula- tion, including sensitivity analysis, optimization, and validation/verification. Sensitivity analysis is divided into two phases. The first phase is a pilot stage, which consists of screening or searching for the important factors among (say) hundreds of potentially important factors. A novel screening technique is presented, namely sequential bifurcation. The second phase uses regression analysis to approximate the input/output transformation that is implied by the simulation model; the resulting regression model is also known as a metamodel or a response surface. Regression analysis gives better results when the simu- lation experiment is well designed, using either classical statistical designs (such as frac- tional factorials) or optimal designs (such as pioneered by Fedorov, Kiefer, and Wolfo- witz). To optimize the simulated system, the analysts may apply Response Surface Metho- dology (RSM); RSM combines regression analysis, statistical designs, and steepest-ascent hill-climbing. To validate a simulation model, again regression analysis and statistical designs may be applied. Several numerical examples and case-studies illustrate how statisti- cal techniques can reduce the ad hoc character of simulation; that is, these statistical techniques can make simulation studies give more general results, in less time. Appendix 1 summarizes confidence intervals for expected values, proportions, and quantiles, in termi- nating and steady-state simulations. Appendix 2 gives details on four variance reduction techniques, namely common pseudorandom numbers, antithetic numbers, control variates or regression sampling, and importance sampling. Appendix 3 describes jackknifing, which may give robust confidence intervals.least squares;distribution-free;non-parametric;stopping rule;run-length;Von Neumann;median;seed;likelihood ratio

Control-friendly scheduling algorithms for multi-tool, multi-product manufacturing systems

textThe fabrication of semiconductor devices is a highly competitive and capital intensive industry. Due to the high costs of building wafer fabrication facilities (fabs), it is expected that products should be made efficiently with respect to both time and material, and that expensive unit operations (tools) should be utilized as much as possible. The process flow is characterized by frequent machine failures, drifting tool states, parallel processing, and reentrant flows. In addition, the competitive nature of the industry requires products to be made quickly and within tight tolerances. All of these factors conspire to make both the scheduling of product flow through the system and the control of product quality metrics extremely difficult. Up to now, much research has been done on the two problems separately, but until recently, interactions between the two systems, which can sometimes be detrimental to one another, have mostly been ignored. The research contained here seeks to tackle the scheduling problem by utilizing objectives based on control system parameters in order that the two systems might behave in a more beneficial manner. A non-threaded control system is used that models the multi-tool, multi-product process in a state space form, and estimates the states using a Kalman filter. Additionally, the process flow is modeled by a discrete event simulation. The two systems are then merged to give a representation of the overall system. Two control system matrices, the estimate error covariance matrix from the Kalman filter and a square form of the system observability matrix called the information matrix, are used to generate several control-based scheduling algorithms. These methods are then tested against more tradition approaches from the scheduling literature to determine their effectiveness on both the basis of how well they maintain the outputs near their targets and how well they minimize the cycle time of the products in the system. The two metrics are viewed simultaneously through use of Pareto plots and merits of the various scheduling methods are judged on the basis of Pareto optimality for several test cases.Chemical Engineerin

A study of self-similar traffic generation for ATM networks

This thesis discusses the efficient and accurate generation of self-similar traffic for ATM networks. ATM networks have been developed to carry multiple service categories. Since the traffic on a number of existing networks is bursty, much research focuses on how to capture the characteristics of traffic to reduce the impact of burstiness. Conventional traffic models do not represent the characteristics of burstiness well, but self-similar traffic models provide a closer approximation. Self-similar traffic models have two fundamental properties, long-range dependence and infinite variance, which have been found in a large number of measurements of real traffic. Therefore, generation of self-similar traffic is vital for the accurate simulation of ATM networks. The main starting point for self-similar traffic generation is the production of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN). In this thesis six algorithms are brought together so that their efficiency and accuracy can be assessed. It is shown that the discrete FGN (dPGN) algorithm and the Weierstrass-Mandelbrot (WM) function are the best in terms of accuracy while the random midpoint displacement (RMD) algorithm, successive random addition (SRA) algorithm, and the WM function are superior in terms of efficiency. Three hybrid approaches are suggested to overcome the inefficiency or inaccuracy of the six algorithms. The combination of the dFGN and RMD algorithm was found to be the best in that it can generate accurate samples efficiently and on-the-fly. After generating FBM sample traces, a further transformation needs to be conducted with either the marginal distribution model or the storage model to produce self-similar traffic. The storage model is a better transformation because it provides a more rigorous mathematical derivation and interpretation of physical meaning. The suitability of using selected Hurst estimators, the rescaled adjusted range (R/S) statistic, the variance-time (VT) plot, and Whittle's approximate maximum likelihood estimator (MLE), is also covered. Whittle's MLE is the better estimator, the R/S statistic can only be used as a reference, and the VT plot might misrepresent the actual Hurst value. An improved method for the generation of self-similar traces and their conversion to traffic has been proposed. This, combined with the identification of reliable methods for the estimators of the Hurst parameter, significantly advances the use of self-similar traffic models in ATM network simulation