Steady flow control for a novel lattice hydrodynamic model with time delay based on discrete‐time system

Abstract

This paper aims to investigate the influence of time delay effect and steady flow control strategy on traffic flow. Consider that the time delay in sensing flux information during the operation of traffic system is inevitable. Meanwhile, a new method is applied to model and analyse traffic system. A novel discrete‐time lattice hydrodynamic model considering time delay is introduced in this paper. Based on the proposed model with constant and varying time‐delay, the asymptotic stabilities are investigated and corresponding stable conditions are derived. The traffic flow evolution trend with and without time delay is conducted and compared by numerical simulations. Also, under the influence of different control gain conditions, density wave characteristics for traffic flow system with time delay are intuitively shown. The results indicate that time delay effect in sensing density and flux information can aggravate traffic congestion, and traffic congestion will be effectively relieved by considering steady flow control signal.