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.

本文提出了一种新的极值分布类别，称为复合广义极值（CGEV）分布，以研究每月和季节性变化对道路网络中极度行驶延迟的影响。由于极端事件的发生频率和严重程度与天气状况的变化高度相关，这是事件和长时间延误的外在原因，因此天气的每月和季节性变化会导致极端旅行时间的变化。驾驶行为的变化本身会根据道路/天气情况而变化，这也会导致观察到的极端旅行时间的每月和季节性变化。因此，至关重要的是对月度和季节变化对道路网络上观察到的极端旅行延误的影响进行建模。根据经验揭示的月度和季节水平极端旅行延误的均值和标准差（SD）之间的线性关系，建立了两个乘性误差模型。然后，通过链接两个乘性误差模型并形成表征极端行进延迟中总体变化的复合分布，来获得CGEV分布。校准了CGEV分布参数，并使用了来自卡尔加里市道路网的多年观测行驶时间数据验证了用于推导CGEV分布的基本假设。结果表明，通过识别季节性特定参数来考虑季节性，可以提供灵活且不太复杂的CGEV分布，其表现要优于传统的GEV分布。最后，建议的CGEV分布的应用是在道路网络脆弱性的情况下进行评估的，同时考虑到观察到的极端事件发生概率和链路重要性。从连接性和旅行需求与供应之间的动态交互方面来看，这种衍生的数据驱动的脆弱性指数包含了与网络拓扑相关的大量信息。因此，这种新的数据驱动的漏洞度量可以用作决策支持工具，以告知决策者优先级对关键链路的改进，以增强总体网络漏洞，可靠性和弹性。从连接性和旅行需求与供应之间的动态交互方面来看，这种衍生的数据驱动的脆弱性指数包含了与网络拓扑相关的大量信息。因此，这种新的数据驱动的漏洞度量可以用作决策支持工具，以告知决策者优先级对关键链路的改进，以增强总体网络漏洞，可靠性和弹性。从连接性和旅行需求与供应之间的动态交互方面来看，这种衍生的数据驱动的脆弱性指数包含了与网络拓扑相关的大量信息。因此，这种新的数据驱动的漏洞度量可以用作决策支持工具，以告知决策者优先级对关键链路的改进，以增强总体网络漏洞，可靠性和弹性。