Statistical Model for Forecasting Link Travel Time Variability

In the field of advanced traveler information systems, travel time reliability contributes significantly to the utility of traffic information affecting the traveler's choice. The exact estimation of the variance in travel times is fundamental to calculating reliability indices. A method for predicting the dynamic variance in estimated link travel times is described. The dynamic variance is allowed to vary dependent on variances for previous time periods, which is typically ignored in conventional time-series analysis. We adopt the autoregressive moving average-generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) model in which the ARMA model and the GARCH model are combined. In parallel, the generalized Pareto distribution (GPD) is employed in the computation of percentile to overcome the asymmetry in travel time distribution. The autocorrelation of dynamic variance is identified in links located in urban congested areas. The use of the ARMA-GARCH model yielded statistically significant outcomes in estimating dynamic variances in travel times. In particular, for a link with higher level of congestion, the ARMA-GARCH model along with GPD has been proven to be more promising.

[1]  David Levinson,et al.  A Moment of Time: Reliability in Route Choice Using Stated Preference , 2010, J. Intell. Transp. Syst..

[2]  Steven I-Jy Chien,et al.  DYNAMIC TRAVEL TIME PREDICTION WITH REAL-TIME AND HISTORICAL DATA , 2003 .

[3]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[4]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[5]  Ruimin Li,et al.  Evaluation of speed-based travel time estimation models , 2006 .

[6]  Adrian Pagan,et al.  Alternative Models for Conditional Stock Volatility , 1989 .

[7]  Huairui Guo,et al.  Travel time estimation using correlation analysis of single loop detector data , 2004 .

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

[9]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[10]  K. West,et al.  The Predictive Ability of Several Models of Exchange Rate Volatility , 1994 .

[11]  David Mahalel,et al.  Time-series model for vehicle speeds , 1985 .

[12]  A. McNeil,et al.  Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach , 2000 .

[13]  Daniel B. Nelson.  Stationarity and Persistence in the GARCH(1,1) Model , 1990, Econometric Theory.

[14]  H. J. Van Zuylen,et al.  Monitoring and Predicting Freeway Travel Time Reliability: Using Width and Skew of Day-to-Day Travel Time Distribution , 2005 .

[15]  E. Hannan,et al.  Recursive estimation of mixed autoregressive-moving average order , 1982 .

[16]  Pravin Varaiya,et al.  Travel-Time Reliability as a Measure of Service , 2003 .

[17]  A. Kemna,et al.  Analysis of the Term Structure of Implied Volatilities , 1994, Journal of Financial and Quantitative Analysis.

[18]  Circadian rhythm analysis when output is collected at intervals. , 1977, Biometrics.

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

[20]  Hironori Suzuki,et al.  Application of Probe-Vehicle Data for Real-Time Traffic-State Estimation and Short-Term Travel-Time Prediction on a Freeway , 2003 .

[21]  Serge P. Hoogendoorn,et al.  Valuation of Different Types of Travel Time Reliability in Route Choice: Large-Scale Laboratory Experiment , 2006 .

[22]  Thijs J. Muizelaar,et al.  Drivers’ Preferences for Traffic Information for Nonrecurrent Traffic Situations , 2007 .

[23]  Steven I-Jy Chien,et al.  Dynamic Freeway Travel-Time Prediction with Probe Vehicle Data: Link Based Versus Path Based , 2001 .

[24]  Haitham Al-Deek,et al.  Travel-Time Prediction for Freeway Corridors , 1999 .

[25]  Huizhao Tu,et al.  Travel time unreliability on freeways: Why measures based on variance tell only half the story , 2008 .