Urban Traffic Jam Simulation Based on the Cell Transmission Model

Abstract

There have been different approaches which have been proposed to understand the mechanism of traffic congestion propagation. In this paper, we use the cell transmission model and apply it to simulate the formation and dissipation of traffic jams at the microscopic level. In particular, our model focuses on jam propagation and dissipation in two-way rectangular grid networks. In the model, the downstream exit of the link is channelized to represent the interactions of vehicles in different directions. We have used traffic jam size and congestion delay to measure jam growth and dispersal. Numerical examples exploring the impact of model parameters on jam growth and congestion delay are provided. The simulation results show that there are two strategies to minimize jam size and reduce time for jam dissipation: (1) reduce the length of channelized area and, (2) allocate the stopline widths for all directions in the same ratio as the demands. Furthermore, we obtain some new results about gridlock and discuss the effect of incident position and link length on jam propagation.

Appendix

In this section, Daganzo’s CTM is extended to formulate three categories of cell inflow.

• 1) Inflow of upstream cells

  Inflow of upstream cells can be calculated by:

  $$y_{a}^{i}(t)=min\left\{n_{a}^{i-1}(t), Q_{a}^{i}(t), w \left(N_{a}^{i}(t)-n_{a}^{i}(t)\right)/v\right\}, 1<i\leq\lambda-I$$

  (15)

  From Eq. (15), we have

  $$y_{ab}^{i}(t)=\phi_{ab}y_{a}^{i}(t), 1<i\leq\lambda-I$$

  (16)

• 2) Inflow of downstream queues area

  We define ${\widetilde{y}}_{ab}(t)$ as the up bound of inflow of downstream queues area for vehicles travelling from link a to link b. We have

  $${\widetilde{y}}_{ab}(t)=min\left\{ \phi_{ab}n_{a}^{\lambda-I}(t), \alpha_{ab}Q_{a}^{\lambda-I+1}(t), w \left(\alpha_{ab}N_{a}^{\lambda-I+1}(t)-n_{ab}^{\lambda-I+1}(t)\right)/v \right\}$$

  (17)

  Because of interference between turning vehicles and ahead vehicles, the total inflow of channelized queues area can be formulated as follows

  $$y_{a}^{\lambda-I+1}(t)=min_{b\in B_{m}}\left\{{\widetilde{y}}_{ab}(t)/\alpha_{ab}\right\}$$

  (18)

  Inflow of each direction can be calculated by Eq. (18), gives

  $$y_{ab}^{\lambda-I+1}(t)=\phi_{ab}y_{a}^{\lambda-I+1}(t)$$

  (19)
  $$y_{ab}^{\lambda-I+1}(t)=\phi_{ab}y_{a}^{\lambda-I+1}(t)$$

  (20)

• 3) Inflow of channelized cells

  $$y_{ab}^{i}(t)=min\left\{n_{ab}^{i-1}(t), \alpha_{ab}Q_{a}^{i}(t), w \left(\alpha_{ab}N_{a}^{i}(t)-n_{ab}^{i}(t)\right)/v\right\}, \lambda-I+1<i\leq\lambda$$

  (21)

  The total inflow of cell i can be calculated by Eq. (21), gives

  $$y_{a}^{i}(t)=\sum\limits_{b\in B_{m}}y_{ab}^{i}(t), \lambda-I+1<i\leq\lambda$$

  (22)