Optimal decomposition of travel times measured by probe vehicles using a statistical traffic flow model

Sparse location measurements of probe vehicles are a promising data source for arterial traffic monitoring. One common challenge in processing this source of data is that vehicles are sampled infrequently (on the order of once per minute), which means that many vehicles will travel several links of the network between consecutive measurements. In this article, we propose an optimal decomposition of path travel times of probe vehicles to link travel times for each link traversed. From a model of arterial traffic dynamics, we derive probability distributions of travel times. We prove that these distributions are mixtures of log-concave distributions and derive convex formulations of the travel time allocation problem. We validate our approach using detailed video camera data from the Next Generation Simulation project (NGSIM).

[1]  M J Lighthill,et al.  ON KINEMATIC WAVES.. , 1955 .

[2]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[4]  F. Webster.  TRAFFIC SIGNAL SETTINGS , 1958 .

[5]  Alan J. Miller.  Settings for Fixed-Cycle Traffic Signals , 1963 .

[6]  A. Prékopa.  On logarithmic concave measures and functions , 1973 .

[7]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

[8]  Abdellah Salhi,et al.  Global Optimization: Deterministic Approaches (2nd Edition) , 1994 .

[9]  C. Daganzo.  THE CELL TRANSMISSION MODEL.. , 1994 .

[10]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[11]  A. A. Zhigli︠a︡vskiĭ,et al.  Stochastic Global Optimization , 2007 .

[12]  Arnaud de La Fortelle,et al.  A Belief Propagation Approach to Traffic Prediction using Probe Vehicles , 2007, 2007 IEEE Intelligent Transportation Systems Conference.

[13]  Michel Bierlaire,et al.  Route choice modeling with network-free data , 2008 .

[14]  Liping Fu,et al.  Decomposing Travel Times Measured by Probe-based Traffic Monitoring Systems to Individual Road Segments , 2008 .

[15]  A. Zhigljavsky.  Stochastic Global Optimization , 2008, International Encyclopedia of Statistical Science.

[16]  Yi Zhang,et al.  Short-term traffic flow forecasting of urban network based on dynamic STARIMA model , 2009, 2009 12th International IEEE Conference on Intelligent Transportation Systems.

[17]  A. Bayen,et al.  Minimal error certificates for detection of faulty sensors using convex optimization , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[18]  Ciyun Lin,et al.  Travel Time Estimate Based on Floating Car , 2009, 2009 Second International Conference on Intelligent Computation Technology and Automation.

[19]  Sivan Toledo,et al.  VTrack: accurate, energy-aware road traffic delay estimation using mobile phones , 2009, SenSys '09.

[20]  Ilsoo Yun,et al.  Comparative evaluation of heuristic optimization methods in urban arterial network optimization , 2009, 2009 12th International IEEE Conference on Intelligent Transportation Systems.

[21]  Yusen Chen,et al.  Using Probe Vehicle Data for Traffic State Estimation in Signalized Urban Networks , 2010 .

[22]  Alexandre M. Bayen,et al.  Using Mobile Phones to Forecast Arterial Traffic through Statistical Learning , 2010 .

[23]  Serge P. Hoogendoorn,et al.  TravRes: A method for high-resolution traffic speed reconstruction using GPS-based travel-times , 2010, 13th International IEEE Conference on Intelligent Transportation Systems.

[24]  Alexandre M. Bayen,et al.  Estimating arterial traffic conditions using sparse probe data , 2010, 13th International IEEE Conference on Intelligent Transportation Systems.

[25]  R. Herring,et al.  A hydrodynamic theory based statistical model of arterial traffic , 2010 .

[26]  Alexandre M. Bayen,et al.  Scaling the mobile millennium system in the cloud , 2011, SoCC.