Compound generalized extreme value distribution for modeling the effects of monthly and seasonal variation on the extreme travel delays for vulnerability analysis of road network

This paper proposes a new class of extreme value distribution called compound generalized extreme value (CGEV) distribution for investigating the effects of monthly and seasonal variation on extreme travel delays in road networks. Since the frequency and severity of extreme events are highly correlated to the variation in weather conditions as an extrinsic cause of incidents and long delays, monthly and seasonal changes in weather contributes to extreme travel time variability. The change in driving behavior, which itself varies according to road/weather conditions, also contributes to the monthly and seasonal variation in observed extreme travel times. Therefore, it is critical to model the effect of monthly and seasonal changes on observed extreme travel delays on road networks. Based on the empirically revealed linear relationship between mean and standard deviation (SD) of extreme travel delays for both monthly and seasonal levels, two multiplicative error models are formulated. The CGEV distribution is then obtained by linking the two multiplicative error models and forming a compound distribution that characterizes the overall variation in extreme travel delay. The CGEV distribution parameters are calibrated and the underlying assumptions that are used to derive the CGEV distribution are validated using multi-year observed travel time data from the City of Calgary road network. The results indicate that accounting for the seasonality by identifying seasonal specific parameters provides a flexible and not too complex CGEV distribution that is shown to outperform the traditional GEV distribution. Finally, the application of the proposed CGEV distribution is evaluated in the context of road network vulnerability taking into account the observed probability of extreme event occurrences and the link importance. This derived data-driven vulnerability index incorporates a wealth of information related to both network topography in terms of connectivity and the dynamic interaction between travel demand and supply. This new data-driven vulnerability measure can thus be used as a decision support tool to inform decision-makers in prioritizing improvements to critical links to enhance overall network vulnerability, reliability, and resilience.