Analysis of Travel Time Distribution for Varying Length of Time Interval

Document Type : Research Article

Authors

1 School of Civil Engineering, Iran University of Science and Technology

2 Civil Engineering School Iran University of Science and Technology

3 Iran University of Science and Technology

4 School of Civil Engineering, Islamic Azad University Tehran Science and Research Branch

Abstract

This study intends to determine the most appropriate distribution for modeling travel time variability. It also aims to explore the effects of the time of day and the length of the analysis  time interval on the type of the best-fit probability distribution function. To this end, four analysis time intervals of different lengths ranging from five minutes to three hours are considered. Subsequently, for each analysis time interval, travel time data collected at different times of day are fitted to 12 common probability distribution functions. The Akaike Information Criterion is then used to evaluate the goodness of fitting and to rank the probability distribution functions. The results of this study indicate that the Gaussian mixture distributions are superior to single distributions to represent travel time distribution. In addition, single probability distribution functions can model the distribution of travel time observations when the length of the time interval is short. Among single probability distribution functions, the burr distribution provides the best fit to the travel time data. The results of this research also show that the type of the best-fit probability distribution function does not change significantly over the time of day.

Keywords

Main Subjects

References

[1]   A. Higatani, T. Kitazawa, J. Tanabe, Y. Suga, R. Sekhar, Y. Asakura, Empirical analysis of travel time reliability measures in Hanshin expressway network, Journal of Intelligent Transportation Systems, 13(1) (2009) 28-38.
[2]  Y. Wang, W. Dong, L. Zhang, D. Chin, M. Papageorgiou, G. Rose, W. Young, Speed modeling and travel time estimation based on truncated normal and lognormal distributions, Transportation Research Record, 2315(1) (2012) 66-72.
[3]   N. Khademi, M. Rajabi, A.S. Mohaymany, M. Samadzad, Day-to-day travel time perception modeling using an adaptive-network-based fuzzy inference system (ANFIS), EURO Journal on Transportation Logistics, 5(1) (2016) 25-52.
[4]  G.C. de Jong, M.C. Bliemer, On including travel time reliability of road traffic in appraisal, Transportation Research Part A: Policy and Practice, 73 (2015) 80-95.
[5]  N. Alemazkoor, M.W. Burris, S.R. Danda, Using empirical data to find the best measure of travel time reliability, Transportation Research Record: Journal of the Transportation Research Board, (2530) (2015) 93-100.
[6] B.Y. Chen, W.H. Lam, A. Sumalee, Q. Li, H. Shao, Z. Fang, Finding reliable shortest paths in road networks under uncertainty, Networks and spatial economics, 13(2) (2013) 123-148.
[7]    A. Sumalee, D.P. Watling, S. Nakayama, Reliable network design problem: case with uncertain demand and total travel time reliability, Transportation Research Record, 1964(1) (2006) 81-90.
[8]  W.H.K. Lam, H. Shao, A. Sumalee, Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply, Transportation Research Part B: Methodological, 42(10) (2008) 890-910.
[9]   C. Carrion, D. Levinson, Value of travel time reliability: A review of current evidence, Transportation Research Part A: Policy and Practice, 46(4) (2012) 720-741.
[10] Z. Li, D.A. Hensher, J.M. Rose, Willingness to pay for travel time reliability in passenger transport: A review and some new empirical evidence, Transportation Research Part E: Logistics and Transportation Review, 46(3) (2010) 384-403.
[11] J. Asensio, A. Matas, Commuters’ valuation of travel time variability, Transportation Research Part E: Logistics and Transportation Review, 44(6) (2008) 1074-1085.
[12] S. Yang, Y.-J. Wu, Mixture models for fitting freeway travel time distributions and measuring travel time reliability, Transportation Research Record: Journal of the Transportation Research Board, (2594) (2016) 95-106.
[13] P.A. Alvarez, A methodology to estimate time varying user responses to travel time and travel time reliability in a road pricing environment, Florida International University, 2012.
[14] Y. Nie, X. Wu, J.F. Dillenburg, P.C. Nelson, Reliable route guidance: A case study from Chicago, Transportation Research Part A: Policy and Practice, 46(2) (2012) 403-419.
[15] B. Yao, P. Hu, X. Lu, J. Gao, M. Zhang, Transit network design based on travel time reliability, Transportation Research Part C: Emerging Technologies, 43 (2014) 233-248.
[16] R. Herman, T. Lam, Trip time characteristics of journeys to and from work, Transportation and traffic theory, 6 (1974) 57-86.
[17] E. Emam, H. AI-Deek,  Using  Real-Life  Dual-Loop  Detector  Data to  Develop  New  Methodology  for  Estimating  Freeway  Travel  Time Reliability, Transportation Research Record: Journal of the Transportation Research Board, 1959 (2006) 140-150.
[18] H.A. Rakha, I.E.-. Shawarby, M. Arafeh, F. Dion, Estimating Path Travel-Time Reliability, in: 2006 IEEE Intelligent Transportation Systems Conference, 2006, pp. 236-241.
[19]    N. Faouzi, M. Maurin, Reliability of travel time under lognormal distribution, in: Proceedings of the Transport Research Board 86th Annual Meeting, Washington D.C., 2007.
[20]    C. Lu, J. Dong, Estimating freeway travel time and its reliability using radar sensor data, Transportmetrica B: Transport Dynamics, 6(2) (2018) 97-114.
[21]    M.M. Rahman, S.C. Wirasinghe, L. Kattan, Analysis of bus travel time distributions for varying horizons and real-time applications, Transportation Research Part C: Emerging Technologies, 86 (2018) 453- 466.
[22]    P. Chen, R. Tong, G. Lu, Y. Wang, Exploring Travel Time Distribution and Variability Patterns Using Probe Vehicle Data: Case Study in Beijing, Journal of Advanced Transportation, 2018 (2018) 1-13.
[23]    M. Rajabi-Bahaabadi, A. Shariat-Mohaymany, M. Babaei, D. Vigo, Reliable vehicle routing problem in stochastic networks with correlated travel times, Operational Research, (2019) 1-32.
[24]    L. Weifeng, D. Zhengyu, G. Gaohua, Research on Travel Time Distribution Characteristics of Expressways in Shanghai, Procedia - Social and Behavioral Sciences, 96 (2013) 339-350.
[25]    S. Susilawati, M.A.P. Taylor, S.V.C. Somenahalli, Distributions of travel time variability on urban roads, Journal of Advanced Transportation, 47(8) (2013) 720-736.
[26]    M.A.P. Taylor, Fosgerau’s travel time reliability ratio and the Burr distribution, Transportation Research Part B: Methodological, 97(Supplement C) (2017) 50-63.
[27]    F. Guo, Q. Li, H. Rakha, Multistate travel time reliability models with skewed component distributions, Transportation Research Record: Journal of the Transportation Research Board, (2315) (2012) 47-53.
[28] Z. Ma, L. Ferreira, M. Mesbah, S. Zhu, Modeling distributions of travel time variability for bus operations, Journal of Advanced Transportation, 50(1) (2016) 6-24.
[29] S. Yang, Y.-J. Wu, Mixture Models for Fitting Freeway Travel Time Distributions and Measuring Travel Time Reliability, Transportation Research Record: Journal of the Transportation Research Board, 2594 (2016) 95-106.
[30] F. Yang, M.-P. Yun, X.-G. Yang, Travel Time Distribution Under Interrupted Flow and Application to Travel Time Reliability, Transportation Research Record: Journal of the Transportation Research Board, 2466 (2014) 114-124.
[31] T. Benaglia, D. Chauveau, D. Hunter, D. Young, mixtools: An R package for analyzing finite mixture models, Journal of Statistical Software, 32(6) (2009) 1-29.
[32] N. Munaiah, F. Camilo, W. Wigham, A. Meneely, M. Nagappan, Do bugs foreshadow vulnerabilities? An in-depth study of the chromium project, Empirical Software Engineering, 22(3) (2017) 1305-1347.
[33] J.A. Hartigan, P.M. Hartigan, The dip test of unimodality, The annals of Statistics, 13(1) (1985) 70-84.
[34] W.H. Kruskal, W.A. Wallis, Use of ranks in one-criterion variance analysis, Journal of the American statistical Association, 47(260) (1952) 583-621.
[35] H. Levene, Robust tests for equality of variances, Contributions to probability and statistics, 1 (1961) 279-292. 
AUT Journal of Civil Engineering
Volume 4, Issue 2
June 2020
Pages 241-248

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