Arriving on time: estimating travel time distributions on large-scale road networks

Most optimal routing problems focus on minimizing travel time or distance traveled. Oftentimes, a more useful objective is to maximize the probability of on-time arrival, which requires statistical distributions of travel times, rather than just mean values. We propose a method to estimate travel time distributions on large-scale road networks, using probe vehicle data collected from GPS. We present a framework that works with large input of data, and scales linearly with the size of the network. Leveraging the planar topology of the graph, the method computes efficiently the time correlations between neighboring streets. First, raw probe vehicle traces are compressed into pairs of travel times and number of stops for each traversed road segment using a `stop-and-go' algorithm developed for this work. The compressed data is then used as input for training a path travel time model, which couples a Markov model along with a Gaussian Markov random field. Finally, scalable inference algorithms are developed for obtaining path travel time distributions from the composite MM-GMRF model. We illustrate the accuracy and scalability of our model on a 505,000 road link network spanning the San Francisco Bay Area.

[1]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[2]  Michael I. Jordan.  Learning in Graphical Models , 1999, NATO ASI Series.

[3]  Michael I. Jordan,et al.  An Introduction to Variational Methods for Graphical Models , 1999, Machine-mediated learning.

[4]  Dimitris Achlioptas,et al.  Database-friendly random projections , 2001, PODS.

[5]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[6]  R. Tibshirani,et al.  On the “degrees of freedom” of the lasso , 2007, 0712.0881.

[7]  Takeo Kanade,et al.  Learning GMRF Structures for Spatial Priors , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[8]  Dmitry M. Malioutov,et al.  Low-Rank Variance Approximation in GMRF Models: Single and Multiscale Approaches , 2008, IEEE Transactions on Signal Processing.

[9]  Christian S. Jensen,et al.  Similarity-based prediction of travel times for vehicles traveling on known routes , 2008, GIS '08.

[10]  Stephen Gould,et al.  Projected Subgradient Methods for Learning Sparse Gaussians , 2008, UAI.

[11]  YANQING CHEN,et al.  Algorithm 8 xx : CHOLMOD , supernodal sparse Cholesky factorization and update / downdate ∗ , 2006 .

[12]  Fangfang Zheng,et al.  Reconstruction of delay distribution at signalized intersections based on traffic measurements , 2010, 13th International IEEE Conference on Intelligent Transportation Systems.

[13]  Sebastien Blandin,et al.  A Tractable Class of Algorithms for Reliable Routing in Stochastic Networks , 2011 .

[14]  Alexandre M. Bayen,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1 Learning the Dynamics of Arterial Traffic From Probe , 2022 .

[15]  A. Bayen,et al.  Author ' s personal copy Arterial travel time forecast with streaming data : A hybrid approach of flow modeling and machine learning , 2012 .

[16]  Nikolas Geroliminis,et al.  Estimation of Arterial Route Travel Time Distribution with Markov Chains , 2012 .

[17]  Shane G. Henderson,et al.  Travel time estimation for ambulances using Bayesian data augmentation , 2013, 1312.1873.

[18]  Nicholas Roy,et al.  Practical Route Planning Under Delay Uncertainty: Stochastic Shortest Path Queries , 2013 .

[19]  Alexandre M. Bayen,et al.  The Path Inference Filter: Model-Based Low-Latency Map Matching of Probe Vehicle Data , 2011, IEEE transactions on intelligent transportation systems (Print).