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Integrating the Directional Effect of Traffic into Geostatistical Approaches for Travel Time Estimation


With the direct linkage to a travel map system, geostatistical techniques have been recently adopted for urban travel time estimation. Some important traffic characteristics of urban transportation networks, however, have not been adequately addressed in these studies. As an improvement over the existing studies, this study incorporates the directional effect of traffic into several commonly used geostatistical models for travel time estimation. We show that model performance can be significantly enhanced when flow specific properties are explicitly considered in constructing the associated interpolation models. The developed methodology is applied to a set of traffic data collected in the city of Tucson, Arizona during the rush hours. Results demonstrate an average of 20 % reduction in RMSE compared with those by the traditional approaches.

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  1. Shen, L.: Freeway Travel Time Estimation and Prediction Using Dynamic Neural Networks. Florida International University, Dissertation (2008)

    Google Scholar 

  2. Leonard II, J.D., Simas de Oliveiria, M.G.: Geoinformatics clears traffic jams—travel-time contours visualize traffic weather. GeoInformatics. 22–25 (2001)

  3. Du, J., Aultman-Hall, L.: Using spatial analysis to estimate link travel times on local roads. Transportation Research Board 2006 Annual Meeting CD-ROM, paper 06–0676 (2006)

  4. Miura, H.: A study of travel time prediction using universal kriging. TOP 18(1), 257–270 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Belomestny, D., Jentsch, V., Schreckenberg, M.: Completion and continuation of nonlinear traffic time series: a probabilistic approach. J. Phys. A Math. Gen. 36, 11369–11383 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu, Y., Goodchild, M.F., Guo, Q., Tian, Y., Wu, L.: Towards a general field model and its order in GIS. Int. J. Geogr. Inf. Sci. 22(6), 623–643 (2008)

    Article  Google Scholar 

  7. Matheron, G.: Principles of geostatistics. Econ. Geol. 58, 1246–1266 (1963)

    Article  Google Scholar 

  8. Journel, A.G., Huijbregts, C.J.: Mining Geostatistics. Aademic Press, London (1978)

    Google Scholar 

  9. Isaaks, E.H., Srivastava, R.M.: An Introduction to Applied Geostatistics. Oxford University Press, New York (1989)

    Google Scholar 

  10. Cressie, N.: Statistics for Spatial Data. Revised Edition. Wiley, New York (1993)

    Google Scholar 

  11. Delhomme, J.P.: Kriging in the hydrosciences. Adv. Water Resour. 1, 251–266 (1978)

    Article  Google Scholar 

  12. Volpi, G., Gambolati, G.: On the use of a main trend for the kriging technique in hydrology. Adv. Water Resour. 1, 345–349 (1978)

    Article  Google Scholar 

  13. Kitanidis, P.K.: Introduction to Geostatistics: Applications in Hydrogeology. Cambridge University Press, Cambridge, U.K. (1997)

    Book  Google Scholar 

  14. Abtew, W., Obeysekera, J., Shih, G.: Spatial analysis for monthly rainfall in south Florida. Water Resour. Bull. 29(2), 179–188 (1993)

    Article  Google Scholar 

  15. Holawe, F., Dutter, R.: Geostatistical study of precipitation series in Australia: time and space. J. Hydrol. 219, 70–82 (1999)

    Article  Google Scholar 

  16. Lajaunie, C.: Local risk estimation for a rare noncontagious disease based on observed frequencies. Note N-36/91/G. Centre de Geostatistique, Fontainebleau, Ecole des Mines de Paris (1991)

  17. Webster, R., Oliver, M.A., Muir, K.R., Mann, J.R.: Kriging the local risk of a rare disease from a register of diagnoses. Geogr. Anal. 26, 168–185 (1994)

    Article  Google Scholar 

  18. Goovaerts, P.: Geostatistical analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging. Int. J. Heal. Geogr. 4, 31 (2005)

    Article  Google Scholar 

  19. Chica-Olmo, J.: Spatial estimation of housing prices and locational rents. Urban Stud. 32(8), 1331–1344 (1995)

    Article  Google Scholar 

  20. Montero-Lorenzo, J.-M., Larraz-Iribas, B.: Estimating commercial property prices: an application of cokriging with housing prices as ancillary information. J. Geogr. Syst. 11, 407–425 (2009)

    Article  Google Scholar 

  21. Huijbregts, C.J., Matheron, G.: Universal kriging (An optimal method for estimating and contouring in trend surface analysis). In proceedings of Ninth International Symposium on Techniques for Decision-Making in the Mineral Industry. In: McGerrigle, J.I. (eds.) The Canadian Institute of Mining and Metallurgy, Special Volume 12, pp. 159–169 (1971)

  22. Myers, D.E.: Matrix formulation of co-kriging. Math. Geol. 14(3), 249–257 (1982)

    Article  MathSciNet  Google Scholar 

  23. Stein, A., Corsten, L.C.A.: Universal kriging and cokriging as a regression procedure. Biometrics 47, 575–587 (1991)

    Article  Google Scholar 

  24. Dia, H.: An object-oriented neural network approach to short-term traffic forecasting. Eur. J. Oper. Res. 131(2), 253–261 (2001)

    Article  MATH  Google Scholar 

  25. Rice, J., van Zwet, E.: A simple and effective method for predicting travel times on freeways. IEEE Trans. Intell. Transp. Syst. 5(3), 200–207 (2004)

    Article  Google Scholar 

  26. Ciuffo, B.F., Punzo, V., Quaglietta, E.: Kriging meta-modelling to verify traffic micro-simulation calibration methods. Transportation Research Board 2011 Annual Meeting CD-ROM, paper 11–0451

  27. Selby, B., Kockelman, K.: Spatial prediction of AADT in unmeasured locations by universal kriging. Transportation Research Board 2011 Annual Meeting CD-ROM, paper 11–1665

  28. Bureau of Public Roads: Traffic Assignment Manual. U.S. Dept. of Commerce, Urban Planning Division, Washington D.C (1964)

    Google Scholar 

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Correspondence to Daoqin Tong.

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Tong, D., Lin, WH. & Stein, A. Integrating the Directional Effect of Traffic into Geostatistical Approaches for Travel Time Estimation. Int. J. ITS Res. 11, 101–112 (2013).

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