WSC 2006 Abstracts

Analysis Methodology B Track

Wednesday 10:30:00 AM 12:00:00 PM
Estimation, Queueing, and Optimization

Chair: Jamie Wieland (Purdue University)

Stochastic Gradient Estimation Using a Single Design Point
Jamie R Wieland and Bruce W Schmeiser (Purdue University)

Using concepts arising in control variates, we propose estimating gradients using Monte Carlo data from a single design point. Our goal is to create a statistically efficient estimator that is easy to implement, with no analysis within the simulation oracle and no unknown algorithm parameters. We compare a simple version of the proposed method to finite differences and simultaneous perturbation, assuming first and second-order linear logic models and response surfaces. Results of the analysis indicate that the proposed gradient estimator is unbiased with variance that is inversely related to the variance of the assumed input model. Compared to the only existing single design-point method, the proposed gradient estimator is advantageous in that its variance is not dependent on the magnitude of the response surface at the design point of interest and also decreases as the simulation run length increases.

Efficient Simulation of Population Overflow in Parallel Queues
Victor F. Nicola and Tatiana S. Zaburnenko (University of Twente)

In this paper we propose a state-dependent importance sampling heuristic to estimate the probability of population overflow in networks of parallel queues. This heuristic approximates the "optimal" state-dependent change of measure without the need for difficult mathematical analysis or costly optimization involved in adaptive methodologies. Comprehensive simulations of networks with an arbitrary number of parallel queues and different traffic intensities yield asymptotically efficient estimates (with relative error increasing sub-linearly in the overflow level) where no other state-independent importance sampling techniques are known to be efficient. The efficiency of the proposed heuristic surpasses those based on adaptive importance sampling algorithms, yet it is easier to determine and implement and scales better for large networks.

The Impact of Ordinal on Response Surface Methodology
Sara Jian Oon (Princeton University) and Loo Hay Lee (National University of Singapore)

Traditionally, Response Surface Methodology (RSM) is cardinal in nature. Ordinal optimization was only introduced recently. Since ordinal optimization has been proven to be successful in certain applications, this paper aims to investigate whether ordinal optimization improves RSM by developing ordinal RSM and comparing it with cardinal RSM in terms of efficiency, accuracy and consistency. Assuming that the performances of systems can be expressed as functions of their parameters, both ordinal and cardinal RSM are simulated for several simple multivariable mathematical functions and the effectiveness of ordinal RSM evaluated. It was found that ordinal does not always improve RSM, especially in functions which exhibit a large gradient change over a small region.

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