Prediction Intervals to Account for Uncertainties in Travel Time Prediction

The accurate prediction of travel times is desirable but frequently prone to error. This is mainly attributable to both the underlying traffic processes and the data that are used to infer travel time. A more meaningful and pragmatic approach is to view travel time prediction as a probabilistic inference and to construct prediction intervals (PIs), which cover the range of probable travel times travelers may encounter. This paper introduces the delta and Bayesian techniques for the construction of PIs. Quantitative measures are developed and applied for a comprehensive assessment of the constructed PIs. These measures simultaneously address two important aspects of PIs: 1) coverage probability and 2) length. The Bayesian and delta methods are used to construct PIs for the neural network (NN) point forecasts of bus and freeway travel time data sets. The obtained results indicate that the delta technique outperforms the Bayesian technique in terms of narrowness of PIs with satisfactory coverage probability. In contrast, PIs constructed using the Bayesian technique are more robust against the NN structure and exhibit excellent coverage probability.

[1]  Haris N. Koutsopoulos,et al.  Non-linear kalman filtering algorithms for on-line calibration of dynamic traffic assignment models , 2006, ITSC.

[2]  Xiaoyan Zhang,et al.  Short-term travel time prediction , 2003 .

[3]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[4]  Graham Currie,et al.  Prediction intervals to account for uncertainties in neural network predictions: Methodology and application in bus travel time prediction , 2011, Eng. Appl. Artif. Intell..

[5]  David J. C. MacKay,et al.  The Evidence Framework Applied to Classification Networks , 1992, Neural Computation.

[6]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[7]  S. Roberts,et al.  Confidence Intervals and Prediction Intervals for Feed-Forward Neural Networks , 2001 .

[8]  G. F. Newell,et al.  Control Strategies for an Idealized Public Transportation System , 1972 .

[9]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[10]  Petros A. Ioannou,et al.  Real-Time Estimation of Travel Times Along the Arcs and Arrival Times at the Nodes of Dynamic Stochastic Networks , 2008, IEEE Transactions on Intelligent Transportation Systems.

[11]  John W. Polak,et al.  Modeling Urban Link Travel Time with Inductive Loop Detector Data by Using the k-NN Method , 2005 .

[12]  J. T. Hwang,et al.  Prediction Intervals for Artificial Neural Networks , 1997 .

[13]  R. D. Veaux,et al.  Prediction intervals for neural networks via nonlinear regression , 1998 .

[14]  Sheau-Chiann Chen,et al.  Computational comparison of the prediction intervals of future observation for three-parameter Pareto distribution with known shape parameter , 2007, Appl. Math. Comput..

[15]  Léon Personnaz,et al.  Construction of confidence intervals for neural networks based on least squares estimation , 2000, Neural Networks.

[16]  Graham Currie,et al.  Using SCATS data to predict bus travel time , 2009 .

[17]  Brian Lee Smith,et al.  Measuring Variability in Traffic Conditions by Using Archived Traffic Data , 2002 .

[18]  Graham Currie,et al.  Using GPS Data to Gain Insight into Public Transport Travel Time Variability , 2010 .

[19]  Tao Lu,et al.  Prediction of indoor temperature and relative humidity using neural network models: model comparison , 2009, Neural Computing and Applications.

[20]  Aidong Adam Ding,et al.  Backpropagation of pseudo-errors: neural networks that are adaptive to heterogeneous noise , 2003, IEEE Trans. Neural Networks.

[21]  Yiguang Liu,et al.  The Reliability of Travel Time Forecasting , 2010, IEEE Transactions on Intelligent Transportation Systems.

[22]  H. J. Van Zuylen,et al.  Accurate freeway travel time prediction with state-space neural networks under missing data , 2005 .

[23]  Bekir Bartin,et al.  Determining the Optimal Configuration of Highway Routes for Real-Time Traffic Information: A Case Study , 2010, IEEE Transactions on Intelligent Transportation Systems.

[24]  Tom Heskes,et al.  Practical Confidence and Prediction Intervals , 1996, NIPS.

[25]  J. Bates,et al.  The valuation of reliability for personal travel , 2001 .

[26]  Konstantinos G. Zografos,et al.  Design and Assessment of an Online Passenger Information System for Integrated Multimodal Trip Planning , 2009, IEEE Transactions on Intelligent Transportation Systems.

[27]  Bin Ran,et al.  Interval prediction for traffic time series using local linear predictor , 2004, Proceedings. The 7th International IEEE Conference on Intelligent Transportation Systems (IEEE Cat. No.04TH8749).

[28]  Saeid Nahavandi,et al.  A prediction interval-based approach to determine optimal structures of neural network metamodels , 2010, Expert Syst. Appl..

[29]  Saeid Nahavandi,et al.  Construction of Optimal Prediction Intervals for Load Forecasting Problems , 2010, IEEE Transactions on Power Systems.

[30]  J. W. C. van Lint,et al.  Online Learning Solutions for Freeway Travel Time Prediction , 2008, IEEE Transactions on Intelligent Transportation Systems.

[31]  Teresa B. Culver,et al.  Bootstrapped artificial neural networks for synthetic flow generation with a small data sample , 2006 .

[32]  H. Liu,et al.  Travel time prediction for urban networks , 2008 .

[33]  Mark Dougherty,et al.  A REVIEW OF NEURAL NETWORKS APPLIED TO TRANSPORT , 1995 .

[34]  Salvador García-Muñoz,et al.  A comparison of different methods to estimate prediction uncertainty using Partial Least Squares (PLS): A practitioner's perspective , 2009 .

[35]  A. Weigend,et al.  Estimating the mean and variance of the target probability distribution , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[36]  Avishai Ceder,et al.  Public Transit Planning and Operation: Theory, Modeling and Practice , 2007 .

[37]  Amir F. Atiya,et al.  Lower Upper Bound Estimation Method for Construction of Neural Network-Based Prediction Intervals , 2011, IEEE Transactions on Neural Networks.

[38]  Mashrur Chowdhury,et al.  Real-Time Highway Traffic Condition Assessment Framework Using Vehicle–Infrastructure Integration (VII) With Artificial Intelligence (AI) , 2009, IEEE Transactions on Intelligent Transportation Systems.

[39]  Larry J. Shuman,et al.  Computing confidence intervals for stochastic simulation using neural network metamodels , 1999 .

[40]  H. J. Van Zuylen,et al.  Bayesian committee of neural networks to predict travel times with confidence intervals , 2009 .

[41]  R. Jeong,et al.  Bus arrival time prediction using artificial neural network model , 2004, Proceedings. The 7th International IEEE Conference on Intelligent Transportation Systems (IEEE Cat. No.04TH8749).

[42]  Haris N. Koutsopoulos,et al.  Nonlinear Kalman Filtering Algorithms for On-Line Calibration of Dynamic Traffic Assignment Models , 2006, IEEE Transactions on Intelligent Transportation Systems.