An Improved Car-Following Model considering Desired Safety Distance and Heterogeneity of Driver’s Sensitivity

We investigate the dynamic performance of traffic flow using a modified optimal velocity car-following model. In the car-following scenarios, the following vehicle must continuously adjust the following distance to the preceding vehicle in real time. A new optimal velocity function incorporating the desired safety distance instead of a preset constant is presented first to describe the abovementioned car-following behavior dynamically. The boundary conditions of the new optimal velocity function are theoretically analyzed. Subsequently, we propose an improved car-following model by combining the heterogeneity of driver’s sensitivity based on the new optimal velocity function and previous car-following model. The stability criterion of the improved model is obtained through the linear analysis method. Finally, numerical simulation is performed to explore the effect of the desired safety distance and the heterogeneity of driver’s sensitivity on the traffic flow. Results show that the proposed model has considerable effects on improving traffic stability and suppressing traffic congestion. Furthermore, the proposed model is compatible with the heterogeneity of driver’s sensitivity and can enhance the average velocity of traffic flow compared with the conventional model. In conclusion, the dynamic performance of traffic flow can be improved by considering the desired safety distance and the heterogeneity of driver’s sensitivity in the car-following model.

An extended car-following model considering random safety distance with different probabilities

Because of the difference in vehicle type or driving skill, the driving strategy is not exactly the same. The driving speeds of the different vehicles may be different for the same headway. Since the optimal velocity function is just determined by the safety distance besides the maximum velocity and headway, an extended car-following model accounting for random safety distance with different probabilities is proposed in this paper. The linear stable condition for this extended traffic model is obtained by using linear stability theory. Numerical simulations are carried out to explore the complex phenomenon resulting from multiple safety distance in the optimal velocity function. The cases of multiple types of safety distances selected with different probabilities are presented. Numerical results show that the traffic flow with multiple safety distances with different probabilities will be more unstable than that with single type of safety distance, and will result in more stop-and-go phenomena.

KdV and Kink-Antikink Solitons in an Extended Car-Following Model

An extended car-following model is proposed in this paper by using the generalized optimal velocity function and considering the multivelocity differences. The stability condition of the model is derived by using the linear stability theory. From the reductive perturbation method and nonlinear analysis, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the traffic behaviors near the neutral stability line and around the critical point, respectively. The corresponding soliton wave and kink-antikink soliton solution are used to describe the different traffic jams. It is found that the generalized optimal velocity function and multivelocity differences consideration can further stabilize traffic flow and suppress traffic jams. The theoretical results are well verified through numerical simulations.

Optimal Velocity Function Minimizing Dissipated Energy Considering All Friction in a Position Control System

In order to help reduce global warming, the amount of dissipated energy of machines should be decreased. The present paper discusses optimal current and velocity functions that minimize the dissipated energy in a servo system with friction of all types. The Coulomb friction of a gear in the servo system is represented by the efficiency of the gear and is assumed to be proportional to the absolute value of the output torque of the motor. Even if the system is nonlinear due to Coulomb friction, an analytical optimal function can be solved by introducing a zero crossing time <I>tc</I>, when the input torque of the gear changes from positive to negative. The influence of the viscous friction upon the optimal zero crossing time <I>tc*</I> is examined by simulations. The energy dissipated with the optimal velocity function is compared to the energy dissipated with a conventional trapezoidal velocity function. The results of the simulations and the experiment indicate that the optimal velocity function can greatly reduce the amount of energy dissipated when the moment of inertia is large.