Deterministic simulation

Abstract: Design and Analysis of Simulation Experiments (DASE)focuses on statistical methods for discrete-event simulation (such as queuing and inventory simulations). In addition, the book discusses DASE for deterministic simulation (such as engineering and physics simulations). The text presents both classic and modern statistical designs. Classic designs (e.g., fractional factorials) assume only a few factors with a few values per factor. The resulting input/output data of the simulation experiment are analyzed through low-order polynomials, which are linear regression (meta) models. Modern designs allow many more factors, possible with many values per factor. These designs include group screening (e.g., Sequential Bifurcation, SB) and space filling designs (e.g., Latin Hypercube Sampling, LHS). The data resulting from these modern designs may be analyzed through low-order polynomials for group screening and various metamodel types (e.g., Kriging) for LHS. Design and Analysis of Simulation Experimentsis an authoritative textbook and reference work for researchers, graduate students, and technical practitioners in simulation. Basic knowledge of simulation and mathematical statistics are expected; however, the book does summarize these basics, for the readers' convenience. In addition, the book provides relatively simple solutions for (a) selecting problems to simulate, (b) how to analyze the resulting data from simulation, and (c) computationally challenging simulation problems.

Abstract: We show that any randomized algorithm that runs in space S and time T and uses poly(S) random bits can be simulated using only O(S) random bits in space Sand time T+ poly(S). A deterministic simulation in space S follows. Of independent interest is our main technical tool : a procedure which extracts randomness from a defective random source using a small additional number of truly random bits.

Abstract: Chernoff-Hoeffding (CH) bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables (r.v.'s). We present a simple technique that gives slightly better bounds than these and that more importantly requires only limited independence among the random variables, thereby importing a variety of standard results to the case of limited independence for free. Additional methods are also presented, and the aggregate results are sharp and provide a better understanding of the proof techniques behind these bounds. These results also yield improved bounds for various tail probability distributions and enable improved approximation algorithms for jobshop scheduling. The limited independence result implies that a reduced amount and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the CH bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routing.