This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the stability of the steady states starting from the model in the one-lane case and extending the results to the generic multi-lane case with the careful design of the lane changing rules. We compare the results with numerical tests, that confirm the predictions of the linear stability analysis and also show that the model is able to reproduce stop & go waves, a typical feature of congested traffic.
Citation: Matteo Piu, Gabriella Puppo. Stability analysis of microscopic models for traffic flow with lane changing[J]. Networks and Heterogeneous Media, 2022, 17(4): 495-518. doi: 10.3934/nhm.2022006
This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the stability of the steady states starting from the model in the one-lane case and extending the results to the generic multi-lane case with the careful design of the lane changing rules. We compare the results with numerical tests, that confirm the predictions of the linear stability analysis and also show that the model is able to reproduce stop & go waves, a typical feature of congested traffic.
Vehicles in single-lane road
Red: curve 11 in the
On the left: all vehicles trajectories, on the right: velocity of vehicle 1
On the left: all vehicles trajectories, on the right: velocity of vehicle 1
On the left: all vehicles trajectories, on the right: velocity of vehicle 1
On the left: all vehicles trajectories, on the right: velocity of vehicle 1
On the left: all vehicles trajectories, on the right: velocity of vehicle 1
On the left: all vehicles trajectories, on the right: velocity of vehicle 1
Components of the vector
Lane change from 1 to 2
Lane change from 2 to 1
Optimal velocity functions
Top: vehicle trajectories in the two lanes. Bottom: number of vehicles versus time
Top: vehicle trajectories in the two lanes. Bottom: number of vehicles versus time
Top: vehicle trajectories in the two lanes. Bottom: number of vehicles versus time
Top: vehicle trajectories in the two lanes. Bottom: number of vehicles versus time
Desired velocity functions
Test (a) - Top: vehicle trajectories in the three lanes. Bottom: number of vehicles versus time
Test (b) - Top: vehicle trajectories in the three lanes. Bottom: number of vehicles versus time
Top: vehicle trajectories in the three lanes. Bottom: number of vehicles versus time