Prediction intervals for travel time on transportation networks

Abstract

Estimating travel-time is essential for making travel decisions in transportation networks. Empirically, single road-segment 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 theoretically challenging. Understanding travel-time distribution can help resolve many fundamental problems in transportation, quantifying travel uncertainty as an example. We develop a novel statistical perspective to specific types of dynamical processes that mimic the behavior of travel time on real-world networks. We show that, under general conditions, travel-time normalized by distance, follows a Gaussian distribution with route-invariant (universal) location and scale parameters. We develop efficient inference methods for such parameters, with which we propose asymptotic universal confidence and prediction intervals of travel time. We further develop our theory to include road-segment level information to construct route-specific location and scale parameter sequences that produce tighter route-specific Gaussian-based prediction intervals. We illustrate our methods with a real-world case study using precollected mobile GPS data, where we show that the route-specific and route-invariant intervals both achieve the 95\% theoretical coverage levels, where the former result in tighter bounds that also outperform competing models.Comment: 24 main pages, 4 figures and 4 tables. This version includes many changes to the previous on