International Journal of Transportation Engineering

International Journal of Transportation Engineering

Evaluating the Effectiveness of Burr Mixtures for Travel Time Reliability Analysis

Document Type : Research Paper

Author
Mojtaba Rajabi-Bahaabadi
Civil engineering department, Yazd university, Yazd, Iran
10.22119/ijte.2025.489786.1681
Abstract
Travel time reliability plays a key role in travelers' decision-making processes and serves as a significant indicator for evaluating road performance. The initial stage of enhancing travel time reliability involves measuring it, which guarantees on-time arrivals and minimizes travel costs. A thorough understanding of travel time distribution is required to accurately measure travel time reliability. Traditionally, travel time has been represented using unimodal distributions. However, recent studies have indicated that travel time distribution is often multimodal. Failing to accurately model travel time distribution can lead to overestimation or underestimation of travel time reliability, resulting in suboptimal solutions in practical applications. This study mainly focuses on examining the effectiveness of six different mixture distributions, namely Burr mixture, Gamma mixture, Inverse Gaussian mixture, Log-normal mixture, Normal mixture, and Weibull mixture, in modeling travel time reliability. The Bayesian information criterion is utilized to compare and select the best model for representing travel time distribution. The results of this study indicate that the Burr mixture model can characterize the travel time distribution more accurately compared to its alternatives. Furthermore, the results show that using burr mixture distributions leads to more accurate estimations of travel time reliability measures compared to single distributions.
Keywords
Travel Time Reliability
Probabilistic Modeling
Mixture Models
- Al-Deek, H., & Emam, E. B. (2006). New methodology for estimating reliability in transportation networks with degraded link capacities. Journal of intelligent transportation systems, 10(3), 117-129.
 
- Alonso-González, M. J., van Oort, N., Cats, O., Hoogendoorn-Lanser, S., & Hoogendoorn, S. (2020). Value of time and reliability for urban pooled on-demand services. Transportation Research Part C: Emerging Technologies, 115, 102621.
 
- Antit, A., Jaoua, A., Layeb, S. B., & Triki, C. (2022). A simulation-based optimization model for the vehicle routing problem with bimodal stochastic travel time distribution. IFAC-PapersOnLine, 55(10), 133-138.
 
- Bhat, C. R., & Sardesai, R. (2006). The impact of stop-making and travel time reliability on commute mode choice. Transportation Research Part B: Methodological, 40(9), 709-730.
- Carrion, C., & Levinson, D. (2012). Value of travel time reliability: A review of current evidence. Transportation Research Part A: Policy and Practice, 46(4), 720-741.
 
- Chen, Z., & Liu, X. C. (2021). Statistical distance-based travel-time reliability measurement for freeway bottleneck identification and ranking. Transportation Research Record, 2675(11), 424-438.
 
- Chootinan, P., Wong, S., & Chen, A. (2005). A reliability‐based network design problem. Journal of Advanced Transportation, 39(3), 247-270.
 
- de Jong, G. C., & Bliemer, M. C. (2015). On including travel time reliability of road traffic in appraisal. Transportation Research Part A: Policy and Practice, 73, 80-95.
 
- Fredriksson, H., Holmgren, J., Dahl, M., & Lövström, B. (2023). A Median-Based Misery Index for Travel Time Reliability. Procedia Computer Science, 220, 162-169.
 
- Ganjkhanloo, A., Shariat Mohaymany, A., Bahaabadi, M. R., & Sayyad, A. (2020). Analysis of Travel Time Distribution for Varying Length of Time Interval. AUT Journal of Civil Engineering, 4(2), 241-248.
 
- Ghavidel, M., Khademi, N., Bahrami Samani, E., & Kieu, L.-M. (2022). A Random Effects Model for Travel-Time Variability Analysis Using Wi-Fi and Bluetooth Data. Journal of Transportation Engineering, Part A: Systems, 148(2), 05021012.
 
- Grün, B., & Leisch, F. (2008). FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters. Journal of Statistical Software, 28(4), 1 - 35.
 
- Hartigan, J. A., & Hartigan, P. M. (1985). The dip test of unimodality. The annals of Statistics, 70-84.
 
- Ho, C. Q., Hensher, D. A., & Wang, S. (2020). Joint estimation of mode and time of day choice accounting for arrival time flexibility, travel time reliability and crowding on public transport. Journal of Transport Geography, 87, 102793.
 
- Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999). Bayesian model averaging: a tutorial. Statistical science, 14(4), 382-417.
 
- Li, B., Krushinsky, D., Van Woensel, T., & Reijers, H. A. (2016). The share-a-ride problem with stochastic travel times and stochastic delivery locations. Transportation Research Part C: Emerging Technologies, 67, 95-108.
 
- Li, H., He, F., Lin, X., Wang, Y., & Li, M. (2019). Travel time reliability measure based on predictability using the Lempel–Ziv algorithm. Transportation Research Part C: Emerging Technologies, 101, 161-180.
 
- Li, Z., Hensher, D. A., & Rose, J. M. (2010). 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), 384-403.
 
- Lomax, T., Schrank, D., Turner, S., & Margiotta, R. (2003). Selecting travel reliability measures. T. Transportation Institute, USA.
 
- Lu, C., & Dong, J. (2018). Estimating freeway travel time and its reliability using radar sensor data. Transportmetrica B: Transport Dynamics, 6(2), 97-114.
 
- Ma, Z., Ferreira, L., Mesbah, M., & Zhu, S. (2016). Modeling distributions of travel time variability for bus operations. Journal of Advanced Transportation, 50(1), 6-24.
 
- Miljkovic, T., & Grün, B. (2016). Modeling loss data using mixtures of distributions. Insurance: Mathematics and Economics, 70, 387-396.
 
- Mishra, S., Tang, L., Ghader, S., Mahapatra, S., & Zhang, L. (2018). Estimation and valuation of travel time reliability for transportation planning applications. Case Studies on Transport Policy, 6(1), 51-62.
 
- Pearson, R. K. (2002). Outliers in process modeling and identification. IEEE Transactions on control systems technology, 10(1), 55-63.
 
- Polus, A. (1979). A study of travel time and reliability on arterial routes. Transportation, 8(2), 141-151.
 
- Pu, W. (2011). Analytic relationships between travel time reliability measures. Transportation Research Record, 2254(1), 122-130.
 
- Rajabi-Bahaabadi, M., Shariat-Mohaymany, A., & Yang, S. (2019). Travel time reliability measures accommodating scheduling preferences of travelers. Transportation Research Record, 2673(4), 708-721.
 
- Ricard, L., Desaulniers, G., Lodi, A., & Rousseau, L.-M. (2024). Increasing schedule reliability in the multiple depot vehicle scheduling problem with stochastic travel time. Omega, 127, 103100.
 
- Saw, K., Katti, B. K., Joshi, G. J., & Kedia, A. (2024). Travel time reliability evaluation using fuzzy-possibility approach: a case study of an Indian city. Transportation Planning and Technology, 1-19.
 
- Shams, K., Asgari, H., & Jin, X. (2017). Valuation of travel time reliability in freight transportation: A review and meta-analysis of stated preference studies. Transportation Research Part A: Policy and Practice, 102, 228-243.
 
- Shen, Y., Xu, J., Wu, X., & Ni, Y. (2019). Modelling travel time distribution and its influence over stochastic vehicle scheduling. Transport, 34(2), 237-249.
 
- Small, K. A., Winston, C., & Yan, J. (2005). Uncovering the distribution of motorists' preferences for travel time and reliability. Econometrica, 73(4), 1367-1382.
 
- Srinivasan, K. K., Prakash, A., & Seshadri, R. (2014). Finding most reliable paths on networks with correlated and shifted log–normal travel times. Transportation Research Part B: Methodological, 66, 110-128.
 
- Taylor, M. (1982). Travel time variability-the case of two public modes. Transportation Science, 16(4), 507-521.
 
- Taylor, M. A. (2017). Fosgerau's travel time reliability ratio and the Burr distribution. Transportation Research Part B: Methodological, 97, 50-63.
 
- Tirachini, A., Hensher, D. A., & Bliemer, M. C. (2014). Accounting for travel time variability in the optimal pricing of cars and buses. Transportation, 41, 947-971.
 
- Tong, P., Yan, Y., Wang, D., & Qu, X. (2021). Optimal route design of electric transit networks considering travel reliability. Computer‐Aided Civil and Infrastructure Engineering, 36(10), 1229-1248.
 
- Van Lint, J., Van Zuylen, H. J., & Tu, H. (2008). Travel time unreliability on freeways: Why measures based on variance tell only half the story. Transportation Research Part A: Policy and Practice, 42(1), 258-277.
- Yang, S., & Wu, Y.-J. (2016). Mixture models for fitting freeway travel time distributions and measuring travel time reliability. Transportation Research Record, 2594(1), 95-106.
 
- Yao, B., Hu, P., Lu, X., Gao, J., & Zhang, M. (2014). Transit network design based on travel time reliability. Transportation Research Part C: Emerging Technologies, 43, 233-248.
 
- Zang, Z., Xu, X., Qu, K., Chen, R., & Chen, A. (2022). Travel time reliability in transportation networks: A review of methodological developments. Transportation Research Part C: Emerging Technologies, 143, 103866.
International Journal of Transportation Engineering
Volume 12, Issue 4 - Serial Number 48
Spring 2025
Pages 2009-2023