Abstract
We propose a method for assessing the accuracy of pseudo-random number sampling methods for evacuation modelling purposes. It consists of a systematic comparison between experimental and generated distributions. The calculated weighted relative error (E w_rel ) is based on the statistical parameters as central moments (mean, standard deviation, skewness and kurtosis) to shape the distribution. The case study involves the Box–Muller transform, the Kernel-Epanechnikov, the Kernel-Gaussian and the Piecewise linear generating samples from eight evacuation datasets fitted against normal, lognormal and uniform distributions. Keeping in mind that the Bos Muller method has two potential sources of error (i.e. distribution fitting and sampling), this method produces plausible results when generating samples from the three types of distributions (E w_rel < 0.30 for normal, lognormal and uniform distributions). We also fund that the Kernel Gaussian and the Kernel Epanechnikov methods are well accurate in generating samples from normal distributions (E w_rel < 0.1) but potentially inaccurate when generating samples from uniform and lognormal distributions (E w_rel > 0.80). Results suggest that the Piecewise linear is the most accurate method (E w_rel = 0.01 normal; E w_rel = 0.04 lognormal; E w_rel = 0.009 uniform). This method has the advantage of sampling directly from empirical datasets i.e. no previous distribution fitting is needed. While the proposed method is used here for evacuation modelling, it can be extended to other fire safety engineering applications.
Highlights
Computer models are being used to simulate, visualize, manipulate and gain information of evacuation process
This paper focuses on Pseudo-random Number Sampling Methods (PNSMs) defined here as a transformation from an independent uniform sample or samples [0,1] to a sample of another given distribution
Given the importance of using random variables and understanding the issues associated with the inputs and the intrinsic algorithms of models, our primary objective in this paper is to provide a comprehensive method for assessing the accuracy of different PNSMs when sampling from evacuation datasets
Summary
Computer models are being used to simulate, visualize, manipulate and gain information of evacuation process. It is greatly accepted that evacuation is a random process due to the variability in occupant characteristics, reactions and behaviours [1,2,3,4]. A key point is the way current and future computer evacuation models address this randomness. Evacuation models may be based upon “best fit curves” to represent a set of data. A distribution giving a close fit is supposed to lead to more accurate predictions. This involves two main issues that can increase or decrease the deviation of the behaviour of the potential-actual evacuation from the desired behaviour of the simulated evacuation
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