Applying Finite Mixture Models to New York City Travel Times
Publication: Journal of Transportation Engineering, Part A: Systems
Volume 146, Issue 5
Abstract
The distribution of travel times in high density urban environments is observed to be multimodal as a result of random demand fluctuations, nonrecurrent incidents, and other interruptions. Conventional travel time measures that use indices from unimodal distributions, such as average speed, cannot accurately reflect true traffic conditions in the network. Finite mixture models (FMMs) are a natural choice to represent the distribution of travel times in such settings. In this study, travel times in Midtown Manhattan collected from radio frequency identification device (RFID) transponders are used to test and validate three FMMs. The three models are the Poisson mixture, the Gaussian mixture, and the Gamma mixture. The first two are fitted using the expectation-maximization algorithm and the third using sparse approximation techniques. The Gaussian and Gamma mixture models are demonstrated as capturing the clustering in the travel time data. The Gamma mixture is demonstrated as being slightly superior in terms of generalizability to out-of-sample test data. This case study indicates the potential for a feasible performance measure of the status of urban traffic that is frequently interrupted by signal controls.
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Data Availability Statement
Some or all of the data, models, or code used during the study were provided by a third party (vehicular travel time data within the Midtown Manhattan project area). Direct requests for these materials may be made to the provider, as indicated in the acknowledgments.
Acknowledgments
This work was supported in part by the NYUAD Center for Interacting Urban Networks (CITIES) and funded by the NYUAD Research Institute and Swiss Re. The authors would also like to thank the New York City Department of Transportation (NYCDOT) and KLD Engineering for their support and the data used to complete the case study. The authors would also like to thank Dr. Wuping Xin of KLD Engineering for his assistance with access to the Midtown data, and Dr. Deepthi Dilip for her assistance with the Gamma mixture method.
References
Al-Deek, H., and E. B. Emam. 2006. “New methodology for estimating reliability in transportation networks with degraded link capacities.” J. Intell. Transp. Syst. 10 (3): 117–129. https://doi.org/10.1080/15472450600793586.
Arezoumandi, M. 2011. “Estimation of travel time reliability for freeways using mean and standard deviation of travel time.” J. Transp. Syst. Eng. Inf. Technol. 11 (6): 74–84. https://doi.org/10.1016/S1570-6672(10)60149-3.
Arroyo, S., and A. Kornhauser. 2007. “Modeling travel time distributions on a road network.” In Proc., 11th World Conf. on Transport Research. Leeds, England: World Conference on Transport Research Society.
Bishop, C. 2006. Pattern recognition and machine learning. New York: Springer.
Chen, K., L. Yu, J. Guo, and H. Wen. 2007. “Characteristics analysis of road network reliability in Beijing based on the data logs from taxis.” In Proc., 86th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research of the National Academies of Sciences, Engineering, and Medicine.
Chen, P., K. Yin, and J. Sun. 2014. “Application of finite mixture of regression model with varying mixing probabilities to estimation of urban arterial travel times.” Transp. Res. Rec. 2442 (1): 96–105. https://doi.org/10.3141/2442-11.
Dandy, G. C., and E. A. McBean. 1984. “Variability of individual travel time components.” J. Transp. Eng. 110 (3): 340–356. https://doi.org/10.1061/(ASCE)0733-947X(1984)110:3(340).
Dempster, A., N. Laird, and D. Rubin. 1977. “Maximum likelihood from incomplete data via the EM algorithm.” J. R. Stat. Soc. Ser. B 39 (1): 1–22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x.
Dilip, D., N. Freris, and S. E. Jabari. 2017. “Sparse estimation of travel time distributions using gamma kernels.” In Proc., 96th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research of the National Academies of Sciences, Engineering, and Medicine.
Falcocchio, J. C., E. S. Prassas, and Z. Xu. 2013. Traveler-oriented traffic performance metrics using real time traffic data from the Midtown-in-Motion (MIM) project in Manhattan, NY. New York: Univ. Transportation Research Center.
Fei, X., Y. Zhang, K. Liu, and M. Guo. 2013. “Bayesian dynamic linear model with switching for real-time short-term freeway travel time prediction with license plate recognition data.” J. Transp. Eng. 139 (11): 1058–1067. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000538.
Fu, F., W. Qian, and H. Dong. 2019. “Estimation of route travel time distribution with information fusion from automatic number plate recognition data.” J. Transp. Eng., Part A 145 (7): 04019029. https://doi.org/10.1061/JTEPBS.0000242.
Golshan Khavas, R., and B. Hellinga. 2018. “Examining the relationship between drivers’ anticipated travel time and previous experienced travel times.” J. Transp. Eng., Part A 144 (3): 04018004. https://doi.org/10.1061/JTEPBS.0000124.
Gong, L., and W. Fan. 2017. “Applying travel-time reliability measures in identifying and ranking recurrent freeway bottlenecks at the network level.” J. Transp. Eng., Part A 143 (8): 04017042. https://doi.org/10.1061/JTEPBS.0000072.
Goodall, N. 2018. “Effect of signal control on bimodal travel time distributions.” In Proc., 97th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research of the National Academies of Sciences, Engineering, and Medicine.
Grant, M., and S. Boyd. 2008. “Graph implementations for nonsmooth convex programs.” In Recent advances in learning and control: Lecture notes in control and information sciences, edited by V. Blondel, S. Boyd, and H. Kimura, 95–110. Berlin: Springer.
Grant, M., and S. Boyd. 2014. “CVX: Matlab software for disciplined convex programming, version 2.1.” Accessed February 25, 2020. http://cvxr.com/cvx.
Guessous, Y., M. Aron, N. Bhouri, and S. Cohen. 2014. “Estimating travel time distribution under different traffic conditions.” Transp. Res. Procedia 3 (1): 339–348. https://doi.org/10.1016/j.trpro.2014.10.014.
Guo, F., H. Rakha, and S. Park. 2010. “Multistate model for travel time reliability.” Transp. Res. Rec. 2188 (1): 46–54. https://doi.org/10.3141/2188-06.
Herman, R., and T. Lam. 1974. “Trip time characteristics of journeys to and from work.” In Proc., 6th Int. Symp. on Transportation and Traffic Theory (ISTTT), 57–86. Sydney, Australia: Elsevier.
Jabari, S. E. 2012. “A stochastic model of macroscopic traffic flow: Theoretical foundations.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Minnesota Twin Cities.
Jabari, S. E., D. Dilip, D. Lin, and B. Thonnam Thodi. 2019. “Learning traffic flow dynamics using random fields.” IEEE Access 7 (1): 130566–130577. https://doi.org/10.1109/ACCESS.2019.2941088.
Jabari, S. E., N. Freris, and D. Dilip. 2020. “Sparse travel time estimation from streaming data.” Transp. Sci. 54 (1): 1–20. https://doi.org/10.1287/trsc.2019.0920.
Jabari, S. E., and H. Liu. 2012. “A stochastic model of traffic flow: Theoretical foundations.” Transp. Res. Part B 46 (1): 156–174. https://doi.org/10.1016/j.trb.2011.09.006.
Jabari, S. E., and H. Liu. 2013. “A stochastic model of traffic flow: Gaussian approximation and estimation.” Transp. Res. Part B 47 (Jan): 15–41. https://doi.org/10.1016/j.trb.2012.09.004.
Jabari, S. E., and L. Wynter. 2016. “Sensor placement with time-to-detection guarantees.” EURO J. Transp. Logist. 5 (4): 415–433. https://doi.org/10.1007/s13676-015-0086-4.
Jabari, S. E., F. Zheng, H. Liu, and M. Filipovska. 2018. “Stochastic Lagrangian modeling of traffic dynamics.” In Proc., 97th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research of the National Academies of Sciences, Engineering, and Medicine.
Jabari, S. E., J. Zheng, and H. Liu. 2014. “A probabilistic stationary speed–density relation based on Newell’s simplified car-following model.” Transp. Res. Part B 68 (Oct): 205–223. https://doi.org/10.1016/j.trb.2014.06.006.
Ko, J., and R. Guensler. 2005. “Characterization of congestion based on speed distribution: A statistical approach using Gaussian mixture model.” In Proc., 84th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research of the National Academies of Sciences, Engineering, and Medicine.
Li, L., and S. E. Jabari. 2019. “Position weighted backpressure intersection control for urban networks.” Transp. Res. Part B 128 (Oct): 435–461. https://doi.org/10.1016/j.trb.2019.08.005.
Li, R., H. Chai, and J. Tang. 2013. “Empirical study of travel time estimation and reliability.” Math. Prob. Eng. 2013: 9. https://doi.org/10.1155/2013/504579.
Martchouk, M., F. Mannering, and D. Bullock. 2010. “Analysis of freeway travel time variability using Bluetooth detection.” J. Transp. Eng. 137 (10): 697–704. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000253.
Mogridge, M., and S. Fry. 1984. “The variability of car journey times on a particular route in central London.” Traffic Eng. Control 25 (10): 510–511.
Montgomery, F., and A. May. 1987. “Factors affecting travel times on urban radial routes.” Traffic Eng. Control 28 (9): 452–511.
Moylan, E. 2014. “Performance of reliability metrics on empirhttps://data.cityofnewyork.us/Transportation/Real-Time-Traffic-Speed-Data/qkm5-nuaqical travel time distributions.” In Proc., 93rd Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research of the National Academies of Sciences, Engineering, and Medicine.
NYCDOT (New York City DOT). 2017. “Real-time traffic speed data.” Accessed February 25, 2020. https://data.cityofnewyork.us/Transportation/Real-Time-Traffic-Speed-Data/qkm5-nuaq.
Polus, A. 1979. “A study of travel time and reliability on arterial routes.” Transp. 8 (2): 141–151. https://doi.org/10.1007/BF00167196.
Pu, W. 2011. “Analytic relationships between travel time reliability measures.” Transp. Res. Rec. 2254 (1): 122–130. https://doi.org/10.3141/2254-13.
Rakha, H. A., I. El-Shawarby, M. Arafeh, and F. Dion. 2006. “Estimating path travel-time reliability.” In Proc., 2006 IEEE Intelligent Transportation Systems Conf. (ITSC’06), 236–241. Toronto: IEEE.
Ramezani, M., and N. Geroliminis. 2012. “On the estimation of arterial route travel time distribution with Markov chains.” Transp. Res. Part B 46 (10): 1576–1590. https://doi.org/10.1016/j.trb.2012.08.004.
Richardson, A., and M. Taylor. 1978. “Travel time variability on commuter journeys.” High Speed Ground Transp. J. 12 (1): 77–79.
Sohn, K., and D. Kim. 2009. “Statistical model for forecasting link travel time variability.” J. Transp. Eng. 135 (7): 440–453. https://doi.org/10.1061/(ASCE)0733-947X(2009)135:7(440).
Susilawati, S., M. Taylor, and S. Somenahalli. 2013. “Distributions of travel time variability on urban roads.” J. Adv. Transp. 47 (8): 720–736. https://doi.org/10.1002/atr.192.
Taylor, M., and S. Somenahalli. 2010. “Travel time reliability and the bimodal travel time distribution for an arterial road.” Road Transp. Res. J. Aust. N. Z. Res. Pract. 19 (4): 37–50.
Tibshirani, R. 1996. “Regression shrinkage and selection via the lasso.” J. R. Stat. Soc. Ser. B 58 (1): 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x.
Wardrop, J. G. 1952. “Road paper. Some theoretical aspects of road traffic research.” Proc. Inst. Civ. Eng. 1 (3): 325–362. https://doi.org/10.1680/ipeds.1952.11259.
Xin, W., J. Chang, S. Muthuswamy, and M. Talas. 2013a. “Midtown in Motion: A new active traffic management methodology and its implementation in New York City.” In Proc., 92nd Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research of the National Academies of Sciences, Engineering, and Medicine.
Xin, W., J. Chang, S. Muthuswamy, M. Talas, and E. Prassas. 2013b. “Multiregime adaptive signal control for congested urban roadway networks.” Transp. Res. Rec. 2356 (1): 44–52. https://doi.org/10.1177/0361198113235600106.
Xu, Z. 2018. “Travel time estimation for congested urban traffic.” Ph.D. dissertation, Tandon School of Engineering, New York Univ.
Yang, F., M.-P. Yun, and X.-G. Yang. 2014. “Travel time distribution under interrupted flow and application to travel time reliability.” Transp. Res. Rec. 2466 (1): 114–124. https://doi.org/10.3141/2466-13.
Zheng, F., S. E. Jabari, H. Liu, and D. Lin. 2018. “Traffic state estimation using stochastic Lagrangian dynamics.” Transp. Res. Part B 115 (Sep): 143–165. https://doi.org/10.1016/j.trb.2018.07.004.
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Published In
Journal of Transportation Engineering, Part A: Systems
Volume 146 • Issue 5 • May 2020
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©2020 American Society of Civil Engineers.
History
Received: Jan 18, 2019
Accepted: Oct 28, 2019
Published online: Mar 12, 2020
Published in print: May 1, 2020
Discussion open until: Aug 12, 2020
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