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Identifying optimal data aggregation interval sizes for link and corridor travel time estimation and forecasting

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Abstract

With the recent increase in the deployment of ITS technologies in urban areas throughout the world, traffic management centers have the ability to obtain and archive large amounts of data on the traffic system. These data can be used to estimate current conditions and predict future conditions on the roadway network. A general solution methodology for identifying the optimal aggregation interval sizes for four scenarios is proposed in this article: (1) link travel time estimation, (2) corridor/route travel time estimation, (3) link travel time forecasting, and (4) corridor/route travel time forecasting. The methodology explicitly considers traffic dynamics and frequency of observations. A formulation based on mean square error (MSE) is developed for each of the scenarios and interpreted from a traffic flow perspective. The methodology for estimating the optimal aggregation size is based on (1) the tradeoff between the estimated mean square error of prediction and the variance of the predictor, (2) the differences between estimation and forecasting, and (3) the direct consideration of the correlation between link travel time for corridor/route estimation and forecasting. The proposed methods are demonstrated using travel time data from Houston, Texas, that were collected as part of the automatic vehicle identification (AVI) system of the Houston Transtar system. It was found that the optimal aggregation size is a function of the application and traffic condition.

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Abbreviations

T :

Time of day index (seconds)

H :

Total time period of interest for travel time estimation (e.g., 60 min)

h :

Index for time period

Δτ :

Aggregation interval size (i.e., Δτ = H/h)

N :

Total number of smaller intervals within a larger interval (=H/Δτ)

P :

Total time period of interest for travel time forecasting

K :

Index for future time periods from current time period h

k :

Total number of smaller time periods required for forecasting future P time period (=P/Δτ)

l :

Link index

L :

Total number of links on the corridor

v(h):

Observed number of AVI vehicles at time period h

v(h,k):

Observed number of AVI vehicles at time period h + k

v l (h,k):

Observed number of AVI vehicles on link l at time period h + k

v ij (h,k):

Observed number of AVI vehicles at time period h + k that travel from link i to j

\( \mathop X\nolimits_{l} \left( h \right) \) :

Random variable for travel time on link l at time period h

\( x^{i} \left( h \right) \) :

Observed link travel time of the i-th vehicle at time period h

\( x_{l}^{i} \left( h \right) \) :

Observed link travel time of the i-th vehicle on link l at time period h

\( E\left( {\mathop x\nolimits^{i} \left( h \right)} \right) = \mathop \mu \nolimits_{{\mathop x\nolimits^{i} \left( h \right)}} \) :

Expected link travel time when the i-th vehicle travels the link during time period h

\( \hat{E}\left( {\mathop x\nolimits^{i} \left( h \right)} \right) = \mathop {\hat{\mu }}\nolimits_{{\mathop x\nolimits^{i} \left( h \right)}} \) :

Estimated mean link travel time when the i-th vehicle travels the link during time period h (kernel estimate in this article)

\( X\left( {h,k} \right) \) :

Random variable for travel time on a link during time period h + k

\( \mathop x\nolimits^{i} \left( {h,k} \right) \) :

Observed link travel time of the i-th vehicle on a link during time period h + k

\( \mathop {\hat{x}}\nolimits^{i} \left( {h,k} \right) \) :

Predicted link travel time of the i-th vehicle on a link during time period h + k. Note that the prediction occurs at time h for k-time periods ahead and therefore \( \mathop {\hat{x}}\nolimits^{i} \left( {5,2} \right) \) would be different than \( \mathop {\hat{x}}\nolimits^{i} \left( {6,1} \right) \)

\( \hat{X}\left( {h,k} \right) \) :

Predicted mean link travel time on a link during time period h + k. The prediction occurs at time h for k-time periods ahead

\( \overline{X} \left( h \right) \) :

Sample mean link travel time on a link at time period h

\( \overline{{X_{C} }} \left( h \right) \) :

Sample mean link travel time on a corridor at time period h

\( E\left( {\overline{X} \left( h \right)} \right) = \mathop \mu \nolimits_{{\overline{X} \left( h \right)}} \) :

Expected sample mean link travel time on a link at time period h

\( \overline{X} \left( H \right) \) :

Observed mean link travel time on a link at larger time period H

\( \overline{X} \left( {h,k} \right) \) :

Observed mean link travel time on a link at time period h + k

Δh :

Time period gap between two links (in terms of Δτ) because of travel time on the first link, \( {\Updelta h = }\left\lfloor {\frac{{\overline{X} \left( h \right)}}{\Updelta \tau }} \right\rfloor . \) Note that the operator \( \left\lfloor x \right\rfloor \) returns the largest integer smaller than or equal to x, i.e., the floor of x

Δh l :

Time period gap between the first link and the l-th link on corridor

\( MSE\left( h \right) \) :

Mean square error (MSE) of link travel time estimation at time period h

\( \hat{M}SE\left( h \right) \) :

Estimated MSE of link travel time estimation at time period h

\( \hat{M}SE\left( h \right)_{{\mathop X\nolimits_{ 1} \mathop X\nolimits_{ 2} }} \) :

Estimated MSE of corridor travel time estimation with two links 1 and 2 at time period h

\( \hat{M}SE\left( h \right)_{{\mathop X\nolimits_{ 1} \mathop X\nolimits_{ 2} \ldots \mathop X\nolimits_{L} }} \) :

Estimated MSE of corridor travel time estimation with L links (1, 2,…L link) at time period h

\( \hat{M}SE\left( H \right) \) :

Estimated MSE of travel time estimation over analysis period H \( \left( {H\,\ge\,h} \right); \)

\( \hat{M}SE\left( {h,k} \right) \) :

Estimated MSE of travel time forecasting at time period h for k-time period ahead forecasting

\( \hat{M}SE\left( {h,P} \right) \) :

Estimated MSE of travel time forecasting at time period t for P future time interval (i.e., as many as 1 ~ K multiple periods forecasting)

\( \hat{M}SE\left( {H,P} \right) \) :

Estimated MSE of travel time forecasting at time period H for P future time interval (i.e., 1 ~ K multiple periods forecasting for each time periods 1 ~ N)

w :

Window size of kernel estimate

m :

Number of observed AVI vehicles during a time window w of kernel estimate

s(t):

Number of seconds during a time window w of kernel estimate

\( f\left( {\mathop x\nolimits^{j} } \right) \) :

Kernel density of the vehicle j

\( \delta \left( {\mathop x\nolimits^{j} } \right) \) :

Indicator of kernel density of vehicle j

References

  • Boyce, D., Rouphail, N., Kirson, A.: Estimation and measurement of link travel times in the ADVANCE Project. IEEE-IEE Vehicle Navigation and Information Systems Conference, Ottawa, Canada, 12-15 October, pp. 62–66 (1993)

  • Dailey, D.J.: Travel time estimation using cross-correlation techniques. Transp. Res. B 27(2), 97–107 (1993)

    Article  Google Scholar 

  • Davis, G.A., Nihan, N.L.: Nonparametric regression and short-term freeway traffic forecasting. J. Transp. Eng. 177(2), 178–188 (1991)

    Article  Google Scholar 

  • Eubank, R.L.: Nonparametric Regression and Spline Smoothing, 2nd edn. Marcel Dekker, New York (1999)

    Google Scholar 

  • Fu, L., Rilett, L.R.: Expected shortest paths in dynamic and stochastic traffic networks. Transp. Res. B 32(7), 499–514 (1998)

    Article  Google Scholar 

  • Gajewski, B., Turner, S., Eisele, B., Spiegelman, C.: ITS data archiving: statistical techniques for determining optimal aggregation widths for inductance loop detectors. Transp. Res. Rec. 1719, 85–93 (2000)

    Article  Google Scholar 

  • Hall, R.: The fastest path through a network with random time-dependent travel time. Transp. Sci. 20(3), 182–188 (1986)

    Article  Google Scholar 

  • Miller Hooks, E.D., Mahmassani, H.S.: Least expected time paths in stochastic, time varying transportation networks. Transp. Sci. 34(4), 198–215 (2000)

    Article  Google Scholar 

  • Okutani, I., Stephanedes, Y.J.: Dynamic prediction of traffic volume through Kalman filtering theory. Transp. Res. B 18(1), 1–11 (1984)

    Article  Google Scholar 

  • Oh, C., Ritchie, S.G., Oh, J.: Exploring the relationship between data aggregation and predictability toward providing better predictive traffic information. Preprint CD-ROM, Transportation Research Board (2005)

  • Park, D.: Multiple path based vehicle routing in dynamic and stochastic transportation networks. Ph.D. Dissertation, Department of Civil Engineering, Texas A and M University, Texas (1998)

  • Park, D., Rilett, L.R.: Forecasting multiple-period freeway link travel time using modular neural networks. Transp. Res. Rec. 1617, 163–170 (1998)

    Article  Google Scholar 

  • Park, D., Rilett, L.R.: Forecasting freeway link travel times with a multilayer feedforward neural network. Comput-Aided Civ. Infrastruct. Eng. 14, 357–367 (1999)

    Article  Google Scholar 

  • Park, D., Rilett, L.R., Han, G.: Spectral basis neural networks for real-time travel time forecasting. ASCE J. Transp. Eng. 125(6), 515–523 (1999)

    Article  Google Scholar 

  • Pattanamekar, P., Park, D., Rilett, L.R., Lee, J., Lee, C.: Dynamic and stochastic shortest path in transportation networks with two components of travel time uncertainty. Transp. Res. C 11, 331–354 (2003)

    Article  Google Scholar 

  • Qiao, F., Wang, X., Yu, L.: Optimizing aggregation level for ITS data based on wavelet decomposition. Preprint CD-ROM, Transportation Research Board (2003)

  • Qiao, F., Wang, X., Yu, L.: Double-sided determination of aggregation level for ITS data. Preprint CD-ROM, Transportation Research Board (2004)

  • Rilett, L.R., Park, D., Gajewski, B.J.: Estimating confidence interval for freeway corridor travel time forecasts. Proceedings of the Sixth World Congress on Intelligent Transportation Systems, Toronto, Canada, 8–12 November (1999)

  • Rilett, L.R., Park, D.: Direct forecasting of freeway corridor travel times using spectral basis neural networks. Transp. Res. Rec. 1752, 140–147 (2001)

    Article  Google Scholar 

  • Srinivasan, K.K., Jovanis, P.P.: Determination of number of probe vehicles required for reliable travel time measurement in urban network. Transp. Res. Rec. 1537, 15–22 (1996)

    Article  Google Scholar 

  • Sen, A., Thakuriah, P., Zhu, X.-Q., Karr, A.: Frequency of probe reports and variance of travel time estimates. ASCE J. Transp. Eng. 123(4), 290–299 (1997)

    Article  Google Scholar 

  • Turner, S.M., Holdner, D.J.: Probe vehicle sample sizes for real-time information: The Houston experience. Proceedings of the Vehicle Navigation and Information Systems Conference, Seattle, Washington, 30 July–2 August, pp. 3–10 (1995)

  • Tarko, A., Rouphail, N.M.: Travel time data fusion in ADVANCE, American Society of Civil Engineers Third International Conference on Applications of Advanced Technologies in Transportation Engineering, Washington, DC, July, pp. 36–42 (1993)

  • Van Arem, B., Van Der Vlist, M.J.M., Muste, M.R., Smulders, S.A.: Travel time estimation in the GERDIEN project. Int. J. Forecast. 13, 73–85 (1997)

    Article  Google Scholar 

  • Van Der Voort, M., Dougherty, M., Watson, S.: Combining Kohonen maps with ARIMA time series models to forecast traffic flow. Transp. Res. C 4(5), 307–318 (1996)

    Article  Google Scholar 

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Acknowledgments

The helpful comments of the two anonymous reviewers are greatly appreciated.

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Authors and Affiliations

  1. Department of Transportation, University of Seoul, 90 Jeonnong, Dongdaemoon, Seoul, Republic of Korea

    Dongjoo Park

  2. Mid-America Transportation Center, University of Nebraska-Lincoln, W339 Nebraska Hall, PO Box 880531, Lincoln, NE, 68588-0531, USA

    Laurence R. Rilett

  3. Department of Biostatistics, University of Kansas School of Medicine, Kansas City, KS, 66160, USA

    Byron J. Gajewski

  4. Department of Statistics, Texas A & M University, 405C Blocker Building, College Station, TX, 77843-3143, USA

    Clifford H. Spiegelman

  5. Department of Transportation, Chonnam National University, San 96-1, Dundeok-dong, Yeosu-si, Jeollanam-do, 550-749, Republic of Korea

    Changho Choi

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  1. Dongjoo Park
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Park, D., Rilett, L.R., Gajewski, B.J. et al. Identifying optimal data aggregation interval sizes for link and corridor travel time estimation and forecasting. Transportation 36, 77–95 (2009). https://doi.org/10.1007/s11116-008-9180-x

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