Average optimal flux difference control for a time-varying delayed lattice hydrodynamic model considering backward-looking effect and ramps

This paper investigates a time-varying delayed lattice model considering backward-looking effect, on-ramp and off-ramp, in which average optimal flux difference is put forward as a control signal. The impacts of backward-looking effect, on-ramp, off-ramp and average optimal flux difference control on traffic stability are investigated by theoretical analysis. Also, the stability criterion is acquired by linear matrix inequality. Numerical simulations are used to visually demonstrate the propagation features of disturbances and the final state of traffic density waves under the influences of the backward-looking effect, on-ramp, off-ramp and control over average optimal flux difference. Results show that the rate of on-ramp has a negative impact on the stability of time-varying delayed traffic system, while the rate of off-ramp has a promoting effect on the stability. In addition, the backward-looking effect and average optimal flux difference control help improve the stability of the time-varying delayed system.