Determining Confidence Intervals, and Convergence, for Parameters in Stochastic Evacuation Models

Abstract

An issue when using stochastic egress models is how many simulations are required to accurately represent the modelled scenario? Engineers are mostly interested in a representative Total Evacuation Time (TET). However, the convergence of the TET may not ensure that the full range of evacuation dynamics has been adequately represented. The average total egress curve (AC) has been suggested as an improved measure. Unfortunately, defining a confidence interval (CI) for the AC is problematic. CIs can robustly quantify the precision of many statistics and have been used to define convergence in egress modelling and other research fields. This paper presents a novel application of bootstrapping, functional analysis measures (FAMs), and a bisection algorithm, to derive three FAM-based CIs representing the precision of the AC. These CIs were tested using a theoretical model to demonstrate the consistency of the coverage probability, the actual percentage of CIs that contain the theoretical parameter, with the nominal 95% confidence level (NCL). For two of the FAMbased CIs, it was found that the coverage probability was between 94.2% and 95.6% for all tested sample sizes between 10 and 4000 simulations. The third FAM-based CI's coverage probability was always greater than the NCL and was a conservative estimate, but this presented no problems in practice. A FAM-based CI may suggest if there is more or less variability in an earlier phase of the evacuation. A convergence scheme based on statistical precision, CI widths, is proposed and verified. The method can be extended to other statistics.

Multifactor Variance Assessment for Determining the Number of Repeat Simulation Runs in Evacuation Modelling

“…A number of methods have been proposed to determine the number of RSR of evacuation modelling results by assessing the variance in results [4,5,14,21] (see Table 2). The method by Ronchi, Reneke and Peacock [21] is described as a method for quantitatively analysing the variance in modelling results in evacuation models.…”

“…The most recently proposed method [4] is also an extension of the first mentioned method. The method complements the method by Ronchi et al [21] by introducing confidence intervals (CIs).…”

“…A practical example is used as a case study rather than adopting a mathematical fictitious case, as done in previous studies [4,21]. This is deemed appropriate given the fact that the factors included are of varying character (rather than only referring to evacuation times).…”

“…The work by Grandison [4] provides a novel extension to the method by Ronchi et al [21] by using the concept of CI. Future work could attempt applying Grandison's [4] approach to multiple factors, in a similar fashion to what has been performed in this paper with the MVA method. The main limitation of the MVA method is the selection of suitable acceptance criteria.…”

“…Previous work has been done in order to suggest methods to determine the number of runs needed in relation to the acceptance criteria and scenario under consideration [4,5,14,21]. However, these methods have mainly focused on considering the overall evacuation time and evacuation curves (time series data) as main output of evacuation models.…”