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Modelling traffic flows and estimating road travel times in transportation network under dynamic disturbances

Abstract

Traffic congestion is a common phenomenon in road transportation networks, especially during peak hours. More accurate prediction of dynamic traffic flows is very important for traffic control and management. However, disturbances caused by the time-varying origin-destination matrix, dynamic route choices, and disruptions make the modelling of traffic flows difficult. Therefore, this study focuses on modelling the dynamic evolution processes of traffic flows under disturbances and estimating dynamic travel times for arbitrary moment. A revised Lighthill–Whitham–Richards (RLWR) model with non-equilibrium states is presented to describe the dynamic traffic states on individual roads, and the ripple-spreading model (RSM) is integrated to investigate the interactions among several shockwaves from multiple roads. We propose a hybrid RLWR–RSM to model the congestion and congestion-recovery propagations in an entire transportation network. After predicting the dynamic traffic flows by the RLWR–RSM, the road travel times for arbitrary moment were estimated. Theoretical analyses indicated that (1) the RLWR–RSM inherits the advantages of macroscopic traffic flow models and integrates the characteristics of both low- and high-order continuum models, and (2) the RLWR–RSM considers multiple disturbances. From numerical experiments with various inputs, the variation in travel times under disturbances was investigated, and this further demonstrated that (1) the modelled dynamic traffic flows have four basic properties, and (2) the experimental results validate the theoretical analyses. In addition, the RLWR–RSM can explain several distinct traffic phenomena. Finally, the estimated travel times can provide decision supports for vehicle navigation.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China: [Grant Numbers 41701452]; The National Key Research and Development Program of China (2017YFB0504203); The Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA19030301).

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Correspondence to Jincheng Jiang.

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Appendices

Appendix 1: The time-varying OD matrix in which the sampling period is 10 minute

See Table 2.

Table 2 The time-varying OD matrix in which the sampling period is 10 minutes

Appendix 2: The time varying OD matrix in which the sampling period is 4 minutes

See Table 3.

Table 3 The time varying OD matrix in which the sampling period is 4 minutes

Appendix 3: The static OD matrix

See Table 4.

Table 4 The static OD matrix

Appendix 4: The route path matrix

See Table 5.

Table 5 The route path matrix, where the elements indicate the next node of \(P^k_{O,D}\)

Appendix 5: The route choices

See Table 6.

Table 6 The route choices, where the elements indicate the percentages of vehicles choosing \(P^k_{O,D}\) at particular time moments

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Jiang, J., Dellaert, N., Van Woensel, T. et al. Modelling traffic flows and estimating road travel times in transportation network under dynamic disturbances. Transportation 47, 2951–2980 (2020). https://doi.org/10.1007/s11116-019-09997-3

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Keywords

  • Traffic flow
  • Disturbance
  • Time-varying OD
  • Route choice
  • Network disruption
  • Dynamic travel time