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 FAM-based 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.
Highlights
A stochastic approach to evacuation simulation [1, 2] is employed in many models [3,4,5,6,7,8] to reflect uncertainty in human behaviour [9]
When calculating the CIMT (Eq 3) with varying confidence level (CL), a 99% CL gains an extra 4% in confidence but requires a 33% increase in confidence interval (CI) width compared to a 95% CL
The overall confidence level is equivalent to P(ERD \ Euclidean Projection Coefficient (EPC) \ Secant Cosine (SC)), i.e. all functional analysis measures (FAMs)-based CIs are simultaneously satisfied, and is likely to be less than the individual CL
Summary
A stochastic approach to evacuation simulation [1, 2] is employed in many models [3,4,5,6,7,8] to reflect uncertainty in human behaviour [9]. They noted that this technique could be adapted to determine convergence based on a required precision and that the methodology could be extended to other suitable statistics of interest and types of egress analysis. Ronchi et al [17] define convergence (i.e. sufficient repeat simulations have been performed) when their five statistics of interest (MT, SD and three functional analysis measures (FAMs) of the average total egress curve (AC)) were all changing by less than their specified tolerances per simulation over a set number of simulations. The convergence behaviour of the AC was used to represent behavioural uncertainty, the uncertainty associated with the stochastic nature of human behaviour, by Ronchi et al. CIs have been demonstrated to accurately and efficiently determine convergence for statistics of interest in egress modelling and other fields of study. Apart from demonstrating the correctness of the methods, that work feeds into a discussion on how to determine appropriate tolerances for the FAM-based CIs of AC
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
