Inference for travel time on transportation networks
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Travel time is essential for making travel decisions in real-world transportation networks. Understanding its distribution can resolve many fundamental problems in transportation. Empirically, single-edge travel-time is well studied, but how to aggregate such information over many edges to arrive at the distribution of travel time over a route is still daunting. A range of statistical tools have been developed for network analysis; tools to study statistical behaviors of processes on dynamical networks are still lacking. This paper develops a novel statistical perspective to specific type of mixing ergodic processes (travel time), that mimic the behavior of travel time on real-world networks. Under general conditions on the single-edge speed (resistance) distribution, we show that travel time, normalized by distance, follows a Gaussian distribution with universal mean and variance parameters. We propose efficient inference methods for such parameters, and consequently asymptotic universal confidence and prediction intervals of travel time. We further develop path(route)-specific parameters that enable tighter Gaussian-based prediction intervals. We illustrate our methods with a real-world case study using mobile GPS data, where we show that the route-specific and universal intervals both achieve the 95% theoretical coverage levels. Moreover, the route-specific prediction intervals result in tighter bounds that outperform competing models.
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