Case Studies
Nov 24, 2021

A Random Effects Model for Travel-Time Variability Analysis Using Wi-Fi and Bluetooth Data

Publication: Journal of Transportation Engineering, Part A: Systems
Volume 148, Issue 2

Abstract

This study examined variations in travel time through a random-effects model using Wi-Fi and Bluetooth data. Previous studies mainly divided a day into discrete time windows and estimated an individual distribution function for each window. However, this overlooks the interrelated nature of travel time among the different time windows of a day. The present research suggests a conditional random-effects model that portrays time-varying travel time as a continuous phenomenon. It was shown that the lognormal probability distribution is the best-fitted unimodal distribution. It was hypothesized that the conditional model with a lognormal distribution as the best-fitting choice associated with random effects, it better fits real data than do existing models in the literature. The proposed model demonstrated a strong relationship between the mean and the standard deviation of travel time, and between these two factors and time of day. The travel time data obtained from Wi-Fi and Bluetooth detectors on a highway section of Tehran, Iran were used as a case study.

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Data Availability Statement

The corresponding author will provide all data and codes that support these findings upon request.

References

Abkowitz, M. D., and I. Engelstein. 1983. “Factors affecting running time on transit routes.” Transp. Res. Part A: Gen. 17 (2): 107–113. https://doi.org/10.1016/0191-2607(83)90064-X.
Adnan, M., U. Gazder, A.-H. Yasar, T. Bellemans, and I. Kureshi. 2021. “Estimation of travel time distributions for urban roads using GPS trajectories of vehicles: A case of Athens, Greece.” Pers. Ubiquitous Comput. 25 (1): 237–246. https://doi.org/10.1007/s00779-020-01369-4.
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.
Aliari, Y., and A. Haghani. 2012. “Bluetooth sensor data and ground truth testing of reported travel times.” Transp. Res. Rec. 2308 (1): 167–172. https://doi.org/10.3141/2308-18.
Badiola, N., S. Raveau, and P. Galilea. 2019. “Modelling preferences towards activities and their effect on departure time choices.” Transp. Res. Part A: Policy Pract. 129 (Nov): 39–51. https://doi.org/10.1016/j.tra.2019.08.004.
Bates, J., J. Polak, P. Jones, and A. Cook. 2001. “The valuation of reliability for personal travel.” Transp. Res. Part E Logist. Transp. Rev. 37 (2–3): 191–229. https://doi.org/10.1016/S1366-5545(00)00011-9.
Benezech, V., and N. Coulombel. 2013. “The value of service reliability.” Transp. Res. Part B Methodol. 58 (Dec): 1–15. https://doi.org/10.1016/j.trb.2013.09.009.
Börjesson, M., J. Eliasson, and J. Franklin. 2012. “Valuations of travel time variability in scheduling versus mean–variance models.” Transp. Res. Part B Methodol. 46 (7): 855–873. https://doi.org/10.1016/j.trb.2012.02.004.
Büchel, B., and F. Corman. 2020. “Review on statistical modeling of travel time variability for road-based public transport.” Front. Built Environ. 6 (Jun): 70. https://doi.org/10.3389/fbuil.2020.00070.
Carrion, C., and D. Levinson. 2012. “Value of travel time reliability: A review of current evidence.” Transp. Res. Part A Policy Pract. 46 (4): 720–741. https://doi.org/10.1016/j.tra.2012.01.003.
Cats, O. 2014. “Regularity-driven bus operation: Principles, implementation and business models.” Transp. Policy 36 (Nov): 223–230. https://doi.org/10.1016/j.tranpol.2014.09.002.
Chen, P., R. Tong, G. Lu, and Y. Wang. 2018. “Exploring travel time distribution and variability patterns using probe vehicle data: Case study in Beijing.” J. Adv. Transp. 2018 (Jan): 1–13. https://doi.org/10.1155/2018/3747632.
Coulombel, N., and A. de Palma. 2014a. “The marginal social cost of travel time variability.” Transp. Res. Part C Emerging Technol. 47 (Oct): 47–60. https://doi.org/10.1016/j.trc.2013.12.004.
Coulombel, N., and A. de Palma. 2014b. “Variability of travel time, congestion, and the cost of travel.” Math. Popul. Stud. 21 (4): 220–242. https://doi.org/10.1080/08898480.2013.836420.
Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. “Maximum likelihood from incomplete data via the EM algorithm.” J. R. Stat. Soc. Ser. B Methodol. 39 (1): 1–22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x.
de Rooij, M., and W. Weeda. 2020. “Cross-validation: A method every psychologist should know.” Adv. Methods Pract. Psychol. Sci. 3 (2): 248–263. https://doi.org/10.1177/2515245919898466.
Dion, F., and H. Rakha. 2006. “Estimating dynamic roadway travel times using automatic vehicle identification data for low sampling rates.” Transp. Res. Part B Methodol. 40 (9): 745–766. https://doi.org/10.1016/j.trb.2005.10.002.
Everitt, B. S. 2014. “Finite mixture distributions.” In Wiley StatsRef: Statistics reference online. New York: Wiley.
Fitzmaurice, G., and G. Verbeke. 2008. “Parametric modeling of longitudinal data: Introduction and overview.” In Longitudinal data analysis, 31–41. Boca Raton, FL: Chapman and Hall/CRC.
Fosgerau, M., and L. Engelson. 2011. “The value of travel time variance.” Transp. Res. Part B Methodol. 45 (1): 1–8. https://doi.org/10.1016/j.trb.2010.06.001.
Fosgerau, M., L. Engelson, and J. P. Franklin. 2014. “Commuting for meetings.” J. Urban Econ. 81 (May): 104–113. https://doi.org/10.1016/j.jue.2014.03.002.
Fosgerau, M., and A. Karlström. 2010. “The value of reliability.” Transp. Res. Part B Methodol. 44 (1): 38–49. https://doi.org/10.1016/j.trb.2009.05.002.
Fosgerau, M., and K. Small. 2017. “Endogenous scheduling preferences and congestion.” Int. Econ. Rev. 58 (2): 585–615. https://doi.org/10.1111/iere.12228.
Gong, Y., M. Abdel-Aty, and J. Park. 2019. “Evaluation and augmentation of traffic data including Bluetooth detection system on arterials.” J. Intell. Transp. Syst. 25 (6): 561–573. https://doi.org/10.1080/15472450.2019.1632707.
Guessous, Y., M. Aron, N. Bhouri, and S. Cohen. 2014. “Estimating travel time distribution under different traffic conditions.” Transp. Res. Procedia 3 (Jan): 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.
Hjorth, K., M. Börjesson, L. Engelson, and M. Fosgerau. 2015. “Estimating exponential scheduling preferences.” Transp. Res. Part B Methodol. 81 (Nov): 230–251. https://doi.org/10.1016/j.trb.2015.03.014.
Jenelius, E. 2012. “The value of travel time variability with trip chains, flexible scheduling and correlated travel times.” Transp. Res. Part B Methodol. 46 (6): 762–780. https://doi.org/10.1016/j.trb.2012.02.003.
Kazemi, I., and R. Crouchley. 2006. “Modelling the initial conditions in dynamic regression models of panel data with random effects.” Chap. 4 in Vol. 274 of Panel data econometrics, edited by B. H. Baltagi, 91–117. Amsterdam, Netherlands: Elsevier.
Kieu, L.-M., A. Bhaskar, and E. Chung. 2015. “Public transport travel-time variability definitions and monitoring.” J. Transp. Eng. 141 (1): 04014068. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000724.
Kim, J., H. S. Mahmassani, P. Vovsha, Y. Stogios, and J. Dong. 2013. “Scenario-based approach to analysis of travel time reliability with traffic simulation models.” Transp. Res. Rec. 2391 (1): 56–68. https://doi.org/10.3141/2391-06.
Koster, P., E. Kroes, and E. Verhoef. 2011. “Travel time variability and airport accessibility.” Transp. Res. Part B Methodol. 45 (10): 1545–1559. https://doi.org/10.1016/j.trb.2011.05.027.
Lam, T., and K. Small. 2001. “The value of time and reliability: Measurement from a value pricing experiment.” Transp. Res. Part E Logist. Transp. Rev. 37 (2–3): 231–251. https://doi.org/10.1016/S1366-5545(00)00016-8.
Li, H., H. Tu, and X. Zhang. 2017. “Travel time variations over time and routes: Endogenous congestion with degradable capacities.” Transportmetrica B: Transp. Dyn. 5 (1): 56–77. https://doi.org/10.1080/21680566.2015.1121846.
Li, Z., and D. Hensher. 2020. “Understanding risky choice behaviour with travel time variability: A review of recent empirical contributions of alternative behavioural theories.” Transp. Lett. 12 (8): 580–590. https://doi.org/10.1080/19427867.2019.1662562.
Li, Z., D. A. Hensher, and J. M. Rose. 2010. “Willingness to pay for travel time reliability in passenger transport: A review and some new empirical evidence.” Transp. Res. Part E Logist. Transp. Rev. 46 (3): 384–403. https://doi.org/10.1016/j.tre.2009.12.005.
Loustau, P., C. Morency, M. Trépanier, and L. Gourvil. 2010. “Travel time reliability on a highway network: Estimations using floating car data.” Transp. Lett. 2 (1): 27–37. https://doi.org/10.3328/TL.2010.02.01.27-37.
Lu, Y., and G.-L. Chang. 2012. “Stochastic model for estimation of time-varying arterial travel time and its variability with only link detector data.” Transp. Res. Rec. 2283 (1): 44–56. https://doi.org/10.3141/2283-05.
Ma, Z., L. Ferreira, M. Mesbah, and S. Zhu. 2015. “Modeling distributions of travel time variability for bus operations.” J. Adv. Transp. 50 (1): 6–24. https://doi.org/10.1002/atr.1314.
Martchouk, M., F. Mannering, and D. Bullock. 2011. “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.
Mazloumi, E., G. Currie, and G. Rose. 2010. “Using GPS data to gain insight into public transport travel time variability.” J. Transp. Eng. 136 (7): 623–631. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000126.
McCulloch, C. E., and J. M. Neuhaus. 2011. “Misspecifying the shape of a random effects distribution: Why getting it wrong may not matter.” Stat. Sci. 26 (3): 388–402. https://doi.org/10.1214/11-STS361.
McCulloch, C. E., S. Searle, and J. Neuhaus. 2001. Generalized, linear, and mixed models. New York: Wiley.
Noland, R. B., and J. W. Polak. 2002. “Travel time variability: A review of theoretical and empirical issues.” Transp. Rev. 22 (1): 39–54. https://doi.org/10.1080/01441640010022456.
Park, S., H. Rakha, and F. Guo. 2011. “Multi-state travel time reliability model: Impact of incidents on travel time reliability.” In Proc., Conf. Record—IEEE Conf. on Intelligent Transportation Systems. New York: IEEE.
Peer, S., C. C. Koopmans, and E. T. Verhoef. 2012. “Prediction of travel time variability for cost-benefit analysis.” Transp. Res. Part A Policy Pract. 46 (1): 79–90. https://doi.org/10.1016/j.tra.2011.09.016.
Peer, S., and E. T. Verhoef. 2013. “Equilibrium at a bottleneck when long-run and short-run scheduling preferences diverge.” Transp. Res. Part B Methodol. 57 (Nov): 12–27. https://doi.org/10.1016/j.trb.2013.09.001.
Polus, A. 1979. “A study of travel time and reliability on arterial routes.” Transportation 8 (2): 141–151. https://doi.org/10.1007/BF00167196.
Pu, Z., M. Zhu, W. Li, Z. Cui, X. Guo, and Y. Wang. 2021. “Monitoring public transit ridership flow by passively sensing Wi-Fi and Bluetooth mobile devices.” IEEE Internet Things J. 8 (1): 474–486. https://doi.org/10.1109/JIOT.2020.3007373.
Rahman, M. M., S. C. Wirasinghe, and L. Kattan. 2018. “Analysis of bus travel time distributions for varying horizons and real-time applications.” Transp. Res. Part C Emerging Technol. 86 (Jan): 453–466. https://doi.org/10.1016/j.trc.2017.11.023.
Rajabi-Bahaabadi, M., A. Shariat-Mohaymany, and S. Yang. 2019. “Travel time reliability measures accommodating scheduling preferences of travelers.” Transp. Res. Rec. 2673 (4): 708–721. https://doi.org/10.1177/0361198119836980.
Rakha, H., I. El-Shawarby, and M. Arafeh. 2010. “Trip travel-time reliability: Issues and proposed solutions.” J. Intell. Transp. Syst. 14 (4): 232–250. https://doi.org/10.1080/15472450.2010.517477.
Saedi, R., and N. Khademi. 2019. “Travel time cognition: Exploring the impacts of travel information provision strategies.” Travel Behav. Soc. 14 (Jan): 92–106. https://doi.org/10.1016/j.tbs.2018.09.007.
Small, K. A. 2012. “Valuation of travel time.” Econ. Transp. 1 (1): 2–14. https://doi.org/10.1016/j.ecotra.2012.09.002.
Soriguera, F. 2014. “On the value of highway travel time information systems.” Transp. Res. Part A Policy Pract. 70 (Dec): 294–310. https://doi.org/10.1016/j.tra.2014.10.005.
Stephens, M. A. 1974. “EDF statistics for goodness of fit and some comparisons.” J. Am. Stat. Assoc. 69 (347): 730–737. https://doi.org/10.1080/01621459.1974.10480196.
Sun, C., G. Arr, and R. P. Ramachandran. 2003. “Vehicle reidentification as method for deriving travel time and travel time distributions: Investigation.” Transp. Res. Rec. 1826 (1): 25–30. https://doi.org/10.3141/1826-04.
Susilawati, S., M. A. P. Taylor, and S. V. C. 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. A. P. 2013. “Travel through time: The story of research on travel time reliability.” Transportmetrica B: Transp. Dyn. 1 (3): 174–194. https://doi.org/10.1080/21680566.2013.859107.
Taylor, M. A. P., and S. Susilawati. 2012. “Modelling travel time reliability with the Burr distribution.” Procedia-Social Behav. Sci. 54 (Oct): 75–83. https://doi.org/10.1016/j.sbspro.2012.09.727.
Torrisi, V., M. Ignaccolo, and G. Inturri. 2017. “Estimating travel time reliability in urban areas through a dynamic simulation model.” Transp. Res. Procedia 27 (Jan): 857–864. https://doi.org/10.1016/j.trpro.2017.12.134.
Wu, L. 2009. Mixed effects models for complex data. London: Chapman and Hall/CRC. https://doi.org/10.1201/9781420074086.
Xiao, Y., N. Coulombel, and A. de Palma. 2017. “The valuation of travel time reliability: Does congestion matter?” Transp. Res. Part B Methodol. 97 (Mar): 113–141. https://doi.org/10.1016/j.trb.2016.12.003.
Yang, S., and Y.-J. Wu. 2016. “Mixture models for fitting freeway travel time distributions and measuring travel time reliability.” Transp. Res. Rec. 2594 (1): 95–106. https://doi.org/10.3141/2594-13.
Yazici, M. A., C. Kamga, and K. C. Mouskos. 2012. “Analysis of travel time reliability in New York city based on day-of-week and time-of-day periods.” Transp. Res. Rec. 2308 (1): 83–95. https://doi.org/10.3141/2308-09.
Zerguini, S., N. Khademi, and J. Shahi. 2011. “Variability of travel time, users’ uncertainty, and trip information: New approach to cost–benefit analysis.” Transp. Res. Rec. 2254 (1): 160–169. https://doi.org/10.3141/2254-17.

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Go to Journal of Transportation Engineering, Part A: Systems
Journal of Transportation Engineering, Part A: Systems
Volume 148Issue 2February 2022

History

Received: Apr 22, 2021
Accepted: Sep 27, 2021
Published online: Nov 24, 2021
Published in print: Feb 1, 2022
Discussion open until: Apr 24, 2022

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Senior Researcher, School of Civil Engineering, College of Engineering, Univ. of Tehran, Tehran 456311155, Iran (corresponding author). ORCID: https://orcid.org/0000-0003-4035-8069. Email: [email protected]
Associate Professor, School of Civil Engineering, College of Engineering, Univ. of Tehran, Tehran 456311155, Iran. ORCID: https://orcid.org/0000-0003-2565-8194. Email: [email protected]
Ehsan Bahrami Samani [email protected]
Associate Professor, Dept. of Statistics, Faculty of Mathematics, Shahid Beheshti Univ., Tehran 1983969411, Iran. Email: [email protected]
Lecturer, Dept. of Civil and Environmental Engineering, Univ. of Auckland, Auckland 1010, New Zealand. ORCID: https://orcid.org/0000-0001-7798-6195. Email: [email protected]

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  • Development of a Machine-Learning-Based Novel Framework for Travel Time Distribution Determination Using Probe Vehicle Data, Data, 10.3390/data8030060, 8, 3, (60), (2023).

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