A stochastic extension of Newell's three-detector method is presented. The method predicts the traffic states at an intermediate location given boundary data from downstream and upstream detectors. The method presented takes into account day-to-day variations in the arrivals, sensor detection errors, and variability in the fundamental diagram parameters. The output is the probabilistic distribution of predicted cumulative counts, which can be used to obtain confidence bounds on any traffic variable. The method is tested with empirical data.
Get full access to this article
View all access options for this article.
References
1.
WangY., and PapageorgiouM.Real-Time Freeway Traffic State Estimation Based on Extended Kalman Filter: A General Approach. Transportation Research Part B, Vol. 39, No. 2, 2005, pp. 141–167.
2.
PapageorgiouM., and BlossevilleJ.Modelling and Real-Time Control of Traffic Flow on the Southern Part of Boulevard Periphérique in Paris: Part I: Modelling.Transportation Research Part A, Vol. 24, No. 5, 1990, pp. 1–19.
3.
MihaylovaL., BoelR., and HegyiA.An Unscented Kalman Filter for Freeway Traffic Estimation. Proc., 11th IFAC Symposium on Control in Transportation Systems, August 2006, Delft, Netherlands, Vol. 11, Part 1, 2006.
4.
MihaylovaL.A Particle Filter for Freeway Traffic Estimation. Proc., 43rd Conference on Decision and Control, Paradise Island, Bahamas, Dec. 2004, pp. 1–19.
5.
BoelR., and MihaylovaL.A Compositional Stochastic Model for Real Time Freeway Traffic Simulation. Transportation Research Part B, Vol. 40, No. 4, 2006, pp. 319–334.
6.
OuQ., Van LintH., and HoogendoornS.Fusing Heterogeneous and Unreliable Data from Traffic Sensors. Studies in Computational Intelligence, Vol. 281, 2010, pp. 511–545.
7.
TreiberM., and HelbingD.Reconstructing the Spatio-temporal Traffic Dynamics from Stationary Detector Data. Cooperative Transportation Dynamics, Vol. 1, 2002, pp. 3.1–3.24.
8.
TreiberM., KestingA., and WilsonR.E.Reconstructing the Traffic State by Fusion of Heterogeneous Data. Computer-Aided Civil and Infrastructure Engineering, Vol. 26, 2011, pp. 408–419.
9.
Van LintJ., and HoogendoornS. P.A Robust and Efficient Method for Fusing Heterogeneous Data from Traffic Sensors on Freeways. Computer-Aided Civil and Infrastructure Engineering, Vol. 25, No. 8, 2010, pp. 596–612.
10.
NewellG. F.A Simplified Theory of Kinematic Waves in Highway Traffic, I: General Theory, II: Queuing at Freeway Bottlenecks, III: Multi-destination flows.Transportation Research Part B, Vol. 27, No. 4, 1993, pp. 281–313.
11.
LighthillM.J., and WhithamG.On Kinematic Waves. I: Flow Movement in Long Rivers. II: A Theory of Traffic Flow on Long Crowded Roads.Proceedings of the Royal Society of London, Series A, Vol. 229, 1955, pp. 281–345.
12.
RichardsP. I.Shockwaves on the Highway. Operations Research, Vol. 4, 1956, pp. 42–51.
13.
DaganzoC. F.A Variational Formulation of Kinematic Wave Theory: Basic Theory and Complex Boundary Conditions. Transportation Research Part B, Vol. 39, No. 2, 2005, pp. 187–196.
14.
DaganzoC. F.A Variational Formulation of Kinematic Waves: Solution Methods. Transportation Research Part B, Vol. 39, No. 10, 2005, pp. 934–950.
15.
FosterJ.An Investigation of the Hydrodynamic Model for Traffic Flow with Particular Reference to the Effect of Various Speed-Density Relationships. Proc., 1st Conference of the Australian Road Research Board, Portland, OR, 1962, pp. 229–257.
16.
CassidyM.J., and WindoverJ.R.Methodology for Assessing Dynamics of Freeway Traffic Flow. In Transportation Research Record 1484, TRB, National Research Council, Washington, D.C., 1995, pp. 73–79.
17.
MunozJ., and DaganzoC.F. Experimental Characterization of Multi-Lane Freeway Traffic Upstream of an Off-Ramp Bottleneck. Technical Report UCB-ITS-PWP-2000-13. Institute of Transportation Studies, University of California, Berkeley, 2000.
18.
AhnS.Growth of Oscillations in Queued Traffic. PhD thesis. Department of Civil Engineering, University of California, Berkeley, 2005.
19.
ChiabautN., BuissonC., and LeclercqL.Fundamental Diagram Estimation Through Passing Rate Measurements in Congestion. IEEE Transactions on Intelligent Transportation Systems, Vol. 10, No. 2, 2009, pp. 355–359.
20.
AhnS., CassidyM., and LavalJ.A.Verification of a Simplified Car-Following Theory. Transportation Research Part B, Vol. 38, No. 5, 2003, pp. 431–440.
21.
WilsonR. E.Mechanisms for Spatio-Temporal Pattern Formation in Highway Traffic Models. Philosophical Transactions of the Royal Society Part A, Vol. 366, No. 1872, 2008, pp. 2017–2032.
22.
ZhengZ., AhnS., ChenD., and LavalJ.Freeway Traffic Oscillations: Microscopic Analysis of Formations and Propagations Using Wavelet Transform. Transportation Research Part B, Vol. 45, No. 9, 2011, pp. 1378–1388.
23.
ChiabautN., LeclercqL., and BuissonC.From Heterogeneous Drivers to Macroscopic Patterns in Congestion. Transportation Research Part B, Vol. 44, No. 2, 2010, pp. 299–308.
24.
MunozJ., and DaganzoC.F.Fingerprinting Traffic from Static Freeway Sensors. Cooperative Transportation Dynamics, Vol. 1, 2002, pp. 1.1–1.11.
