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Open Access Research Article

Travel time distribution estimation on arterial networks under the stationary conditions

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pp. 59–79Vol. 23Issue 1 & 2November 2025DOI: 10.47974/JDSGT-2024-11016XML
Received:
05 Nov 2024
Published Online:
29 Nov 2025
Article type:
Research Article
Language:
EN
Article no.:
JDSGT-2024-11016
Pages:
59–79

Abstract

Travel time estimation is a challenging task due to the lots of influential factors. The most pre-existing travel time literature assumes travel time follows a specified distribution. Their goal is to find the best fit distribution of travel time based on the observed travel times. Obviously, the role of some influential factors such as intersection signal times, demand variations, supply variations (changing network topology) etc., are neglected.  In this paper, the uncertainty of time and its variations which are consequences of numerous stochastic elements such as uncertain travel demand, uncertain driver behaviors, and random arrival time is modelled by calculating  the probability density function of travel time on each arterial link. Also, the concept of queuing theory is used to take the stochastic features and queue formation behind intersection signals into account;  Additionally, unlike previous model-based methods, the queue of vehicles is modeled as a horizontal queue, and its effects on the travel time are accurately calculated. Also this method is particularly useful  in scenarios  where, due to changes in the network, the previous data may not be highly reliable or in special situations which there is only an estimate of supply and demand such as, the closure of a street or changes in traffic signal timing or large sporting events or emergency situations etc. Eventually, the proposed model is validated and examined by comparison with micro-simulation experiments.

Keywords

Subject Classifications

Primary 90B20Secondary 90C3590C90

References

[1] C. Carrion and D. Levinson, “Value of travel time reliability: A review of current evidence,” Transportation Research Part A: Policy and Practice, vol. 46, no. 4, pp. 720–741 (2012).
[2] M. Kouwenhoven, G. C. de Jong, P. Koster, V. A. C. van den Berg, E. T. Verhoef, J. Bates, and P. M. J. Warffemius, “New values of time and reliability in passenger transport in The Netherlands,” Research in Transportation Economics, vol. 47, pp. 37–49 (2014).
[3] S. Peer, C. C. Koopmans, and E. T. Verhoef, “Prediction of travel time variability for cost-benefit analysis,” Transportation Research Part A: Policy and Practice, vol. 46, no. 1, pp. 79–90 (2012).
[4] F. Zheng and H. Van Zuylen, “Uncertainty and Predictability of Urban Link Travel Time,” Transportation Research Record: Journal of the Transportation Research Board, vol. 2192, pp. 136–146 (2010).
[5] X. Wu and H. X. Liu, “A shockwave profile model for traffic flow on congested urban arterials,” Transportation Research Part B: Methodological, vol. 45, no. 10, pp. 1768–1786 (2011).
[6] F. Zheng, H. Van Zuylen, and X. Liu, “A Methodological Framework of Travel Time Distribution Estimation for Urban Signalized Arterial Roads,” Transportation Science, vol. 51, no. 3, pp. 893–917 (2017).
[7] T. Van Woensel, L. Kerbache, H. Peremans, and N. Vandaele, “Vehicle routing with dynamic travel times: A queueing approach,” European Journal of Operational Research, vol. 186, no. 3, pp. 990–1007 (2008).
[8] E. Jenelius and H. N. Koutsopoulos, “Travel time estimation for urban road networks using low frequency probe vehicle data,” Transportation Research Part B: Methodological, vol. 53, pp. 64–81 (2013).
[9] W. Qin, X. Ji, and F. Liang, “Estimation of urban arterial travel time distribution considering link correlations,” Transportmetrica A: Transport Science, vol. 16, no. 3, pp. 1429–1458 (2020).
[10] D. Bertsimas, A. Delarue, P. Jaillet, and S. Martin, “Travel Time Estimation in the Age of Big Data,” Operations Research, vol. 67, no. 2, pp. 498–515 (2019).
[11] M. Ramezani and N. Geroliminis, “On the estimation of arterial route travel time distribution with Markov chains,” Transportation Research Part B: Methodological, vol. 46, no. 10, pp. 1576–1590 (2012).
[12] P. Cao, T. Miwa, and T. Morikawa, “Modeling Distribution of Travel Time in Signalized Road Section Using Truncated Distribution,” Procedia - Social and Behavioral Sciences, vol. 138, pp. 137–147 (2014).
[13] M. A. P. Taylor and Susilawati, “Modelling Travel Time Reliability with the Burr Distribution,” Procedia - Social and Behavioral Sciences, vol. 54, pp. 75–83 (2012).
[14] M. Beaud, T. Blayac, and M. Stéphan, “Value of Travel Time Reliability: Two Alternative Measures,” Procedia - Social and Behavioral Sciences, vol. 54, pp. 349–356 (2012).
[15] F. Zheng, W. Li, M. van Zuylen, and H. van Zuylen, “Urban travel time reliability at different traffic conditions,” Journal of Intelligent Transportation Systems, vol. 22, no. 2, pp. 106–120 (2018).
[16] N. Geroliminis and A. Skabardonis, “Identification and Analysis of Queue Spillovers in City Street Networks,” IEEE Transactions on Intelligent Transportation Systems, vol. 12, no. 4, pp. 1107–1115 (2011).
[17] C. F. Daganzo, “The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory,” Transportation Research Part B: Methodological, vol. 28, no. 4, pp. 269–287 (1994).
[18] Z. Ghandeharioun and A. Kouvelas, “Link Travel Time Estimation for Arterial Networks Based on Sparse GPS Data and Considering Progressive Correlations,” IEEE Open Journal of Intelligent Transportation Systems, vol. 3, pp. 679–694 (2022).
[19] R. Li, Z. Hao, X. Yang, X. Yang, Y. Wang, Y. Su, and Z. Dong, “Urban road travel time prediction based on gated recurrent unit using internet data,” IET Intelligent Transport Systems, vol. 17, no. 12, pp. 2396–2409 (2023).
[20] M. Gendreau, G. Ghiani, and E. Guerriero, “Time-dependent routing problems: A review,” Computers & Operations Research, vol. 64, pp. 189–197 (2015), doi: 10.1016/j.cor.2015.06.001.
[21] J. Y. Cheah and J. M. G. Smith, “Generalized M/G/C/C state dependent queueing models and pedestrian traffic flows,” Queueing Systems, vol. 15, no. 1–4, pp. 365–386 (1994).
[22] R. Jain and J. M. Smith, “Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models,” Transportation Science, vol. 31, no. 4, pp. 324–336 (1997).
[23] X. Chen, C. Osorio, and B. F. Santos, “Simulation-Based Travel Time Reliable Signal Control,” Transportation Science, vol. 53, no. 2, pp. 523–544 (2019).
[24] F. Zheng and H. Van Zuylen, “Modeling Variability of Urban Travel Times by Analyzing Delay Distribution for Multiple Signalized Intersections,” Transportation Research Record, vol. 2259, no. 1, pp. 80–95 (2011).
[25] C. Osorio and C. Wang, “On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach,” Transportation Research Part B: Methodological, vol. 95, pp. 305–339 (2017).
[26] F. Viti, ‘The Dynamics and the Uncertainty of Delays at Signals’, Doctor of Philosophy, Delft University of Technology, Delft (2006).

[27] C. Osorio and M. Bierlaire, “An analytic finite capacity queueing network model capturing the propagation of congestion and blocking,” European Journal of Operational Research, vol. 196, no. 3, pp. 996–1007 (2009).
[28] P. P. Bocharov, C. D’Apice, and A. V. Pechinkin, Queueing Theory, De Gruyter (2011).
[29] R. S. Kenett, “Fundamentals of queueing theory,” Journal of the Royal Statistical Society: Series D (The Statistician), vol. 35, no. 5, p. 570 (1986), doi: 10.2307/2987982.
[30] O. C. Ibe, Markov Processes for Stochastic Modeling, 2nd ed. Amsterdam, Netherlands: Elsevier, pp. 1–494 (2013), doi: 10.1016/C2012-0-06106-6.
[31] L. A. Elefteriadou, Highway Capacity Manual 6th Edition, The National Academies Press (2016).
[32] Synchro Studio 8 User Guide, Trafficware (2011).
[33] D. Husch and J. Albeck, Trafficware SYNCHRO 6 User Guide, Trafficware (2004).

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