Scenario-based approaches provide an effective and practical approach for capturing the probabilisticnature of travel time in a traffic network. Scenarios that represent daily roadway conditions are generatedby identifying various demand- and supply-side factors that affect travel time variability, and sampling aset of mutually consistent combinations of the associated events. The sampled scenarios are thenevaluated using network simulation models to obtain travel time distributions that provide a basis forextracting a wide range of reliability performance metrics. A key question under this framework pertainsto the number of input scenarios needed to achieve the best estimators of the reliability measures ofinterest given a limited computational budget. Given a stratification of the entire domain of dailyscenarios into distinct scenario categories (or strata), the study addresses the optimal sample sizeallocation problem in connection with stratified sampling. Existing sample allocation schemes, e.g.Neyman’s, are optimized for estimation of the mean. However, dispersion measures such as variance orstandard deviation are of greater concern for reliability analysis. Thus this study explicitly specifies theoptimal allocation scheme for the estimation of the variance. Using a specific characteristic observed intravel time data, namely, a strong positive correlation between standard deviation and mean, an analyticalformula that approximates the variance of the sample variance is developed and an analytical approximatesolution for the optimal allocation for estimating the variance is derived. The proposed method isvalidated using a simulation study and compared with other allocation methods in terms of the estimationof various reliability measures.
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