Route-level travel time reliability requires characterizing the distribution of total travel time across correlated segments -- a problem where existing methods either assume independence (fast but miscalibrated) or model dependence via copulas and simulation (accurate but expensive). We propose a conjugate Bayesian dynamic Gamma model with a common random environment that resolves this trade-off. Each segment's travel time follows a Gamma distribution conditional on a shared latent environment process that evolves as a Markov chain, inducing cross-segment dependence while preserving conditional independence. A moment-matching approximation yields a closed-form $F$-distribution for route travel time, from which the Planning Time Index, Buffer Index, and on-time probability are computed instantly -- at the same $O(1)$ cost as independence-based methods. The conjugate structure ensures that Bayesian posterior updates and the full predictive distribution are available in closed form as new sensor data arrives. Applied to 16 sensors spanning 8.26 miles on I-55 in Chicago, the model achieves 95.4% coverage of nominal 90\% predictive intervals versus 34--37% for independence-based convolution, at identical computational cost.

翻译：路径级行程时间可靠性分析需要刻画相关路段总行程时间的分布特性——现有方法要么假设路段间相互独立（计算快速但校准失准），要么通过copula和仿真建模依赖性（精度高但计算昂贵）。本文提出一种具有共同随机环境的共轭贝叶斯动态伽马模型，以解决这一权衡问题。每个路段的行程时间服从伽马分布，其条件依赖于一个遵循马尔可夫链演化的共享潜环境过程，在保持条件独立性的同时诱导跨路段依赖性。通过矩匹配近似，我们得到了路径行程时间的闭式$F$分布，据此可即时计算计划时间指数、缓冲指数和准时概率——其计算成本与基于独立性的方法相同，均为$O(1)$。共轭结构确保贝叶斯后验更新和完整预测分布在新传感器数据到达时均能以闭式形式获得。将该模型应用于芝加哥I-55公路上覆盖8.26英里的16个传感器数据，在相同计算成本下，其名义90%预测区间的覆盖率达到95.4%，而基于独立性的卷积方法仅达到34-37%。