Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment

In recent years, the traffic congestion problem has become more and more serious, and the research on traffic system control has become a new hot spot. Studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable pivots can alleviate the traffic congestion problem from a new perspective. In this work, the full-speed differential model considering the vehicle network environment is improved in order to adjust the traffic flow from the perspective of bifurcation control, the existence conditions of Hopf bifurcation and saddle-node bifurcation in the model are proved theoretically, and the stability mutation point for the stability of the transportation system is found. For the unstable bifurcation point, a nonlinear system feedback controller is designed by using Chebyshev polynomial approximation and stochastic feedback control method. The advancement, postponement, and elimination of Hopf bifurcation are achieved without changing the system equilibrium point, and the mutation behavior of the transportation system is controlled so as to alleviate the traffic congestion. The changes in the stability of complex traffic systems are explained through the bifurcation analysis, which can better capture the characteristics of the traffic flow. By adjusting the control parameters in the feedback controllers, the influence of the boundary conditions on the stability of the traffic system is adequately described, and the effects of the unstable focuses and saddle points on the system are suppressed to slow down the traffic flow. In addition, the unstable bifurcation points can be eliminated and the Hopf bifurcation can be controlled to advance, delay, and disappear,so as to realize the control of the stability behavior of the traffic system, which can help to alleviate the traffic congestion and describe the actual traffic phenomena as well.

Modeling of Spacing Distribution of Queuing Vehicles at Signalized Junctions Using Random-Matrix Theory

The modeling of headway/spacing between two consecutive vehicles in a queue has many applications in traffic flow theory and transport practice. Most known approaches have only studied vehicles on freeways. This paper presents a model for the spacing distribution of queuing vehicles at a signalized junction based on random-matrix theory. The spacing distribution of a Gaussian symplectic ensemble （GSE） fits well with recently measured spacing distribution data. These results are also compared with measured spacing distribution observed for the car parking problem. Vehicle stationary queuing and vehicle parking have different spacing distributions due to different driving patterns.

Comparison of Vehicle Departure Headways in Beijing and Atlanta

Two characteristics of traffic flows make the vehicle departure headways in Beijing, China different from that in Atlanta, USA. Urban traffic flows in China are often hindered by pedestrians at intersections and queuing vehicles often cannot be totally discharged during the green time, so most signalized intersections are over-saturated in the day time. The first characteristic makes the departure headways of the first and second vehicles in Beijing depend heavily on the start-up situations （with or without interference）. The departure headways of the 3rd to 5th vehicles in Beijing have similar characteristics to those in Atlanta. The second characteristic makes the departure headways after the 5th vehicle significantly different from those in Atlanta. These comparisons show that the conventional delay estimate methods and signal control algorithms may not fit Chinese scenarios, which makes imported intelligent traffic control systems not work well in China without calibrations.

Delay Estimates of Mixed Traffic Flow at Signalized Intersections in China

Two characteristics of Chinese mixed traffic invalidate the conventional queuing delay estimates for western countries. First, the driving characteristics of Chinese drivers lead to different delays even though the other conditions are the same. Second, urban traffic flow in China is often hindered by pedestrians at intersections, such that imported intelligent traffic control systems do not work appropriately. Typical delay estimates for Chinese conditions were obtained from data for over 500 vehicle queues in Beijing collected using charge coupled device （CCD） cameras. The results show that the delays mainly depend on the pro- portion and positions of heavy vehicles in the queue, as well as the start-up situations （with or without interference）. A simplified delay estimation model considers vehicle types and positions that compares well with the observed traffic delays.