<p>This study proposes a vine copula-based framework for estimating bus route travel time distributions, explicitly capturing dependencies between running times and dwell times. Regular vine copulas are used to represent the dependence structure among the components of bus route travel time. The accuracy of simplified truncated forms of vine copulas is also evaluated at different truncation levels. The proposed framework is applied to automatic vehicle location data collected from two urban bus routes in Tehran, Iran. Results demonstrate that the vine copula-based approach substantially improves the accuracy of estimating bus route travel time distributions compared with the convolution model that assumes independence among travel time components. Specifically, for the first route, the Kullback–Leibler divergence decreases from 0.5 under the convolution model to 0.02 using the vine copula approach. For the second route, it decreases from 0.3 to 0.02, indicating a better fit to empirical distributions. Furthermore, the Kolmogorov–Smirnov test confirms that the vine copula-based method can accurately estimate bus route-level travel time distributions at the 95% confidence level. The findings of this paper highlight the importance of modeling dependencies among running time and dwell time variables and demonstrate that the proposed framework provides an effective approach for evaluating bus service reliability.</p>

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A Vine Copula-Based Approach for Estimating Bus Route Travel Time Distributions

  • Mojtaba Rajabi-Bahaabadi

摘要

This study proposes a vine copula-based framework for estimating bus route travel time distributions, explicitly capturing dependencies between running times and dwell times. Regular vine copulas are used to represent the dependence structure among the components of bus route travel time. The accuracy of simplified truncated forms of vine copulas is also evaluated at different truncation levels. The proposed framework is applied to automatic vehicle location data collected from two urban bus routes in Tehran, Iran. Results demonstrate that the vine copula-based approach substantially improves the accuracy of estimating bus route travel time distributions compared with the convolution model that assumes independence among travel time components. Specifically, for the first route, the Kullback–Leibler divergence decreases from 0.5 under the convolution model to 0.02 using the vine copula approach. For the second route, it decreases from 0.3 to 0.02, indicating a better fit to empirical distributions. Furthermore, the Kolmogorov–Smirnov test confirms that the vine copula-based method can accurately estimate bus route-level travel time distributions at the 95% confidence level. The findings of this paper highlight the importance of modeling dependencies among running time and dwell time variables and demonstrate that the proposed framework provides an effective approach for evaluating bus service reliability.