An instantaneous kinematic wave theory of diverging traffic
► The kinematic wave model of non-cooperative diverging traffic is decoupled into nonlinear resonant systems instantaneously. ► A new partial demand function is defined for the Cell Transmission Model. ► Numerical results demonstrate that the model converges and the First-In-First-Out principle is satisfied after a long time. ► It is demonstrated that non-cooperative diverging behaviors lead to reduced network capacities. Diverging junctions are an important type of bottlenecks, which can reduce capacities and initiate and propagate traffic congestion in a road network. In this paper, we propose a kinematic wave theory for modeling dynamics of non-cooperative diverging traffic, in which traffic dynamics of vehicles to one direction are assumed to be independent of those to other directions instantaneously. During a short time interval, the kinematic wave model of diverging traffic is decoupled into a number of nonlinear resonant systems. From analytical solutions to the Riemann problem of a decoupled system, a new definition of partial traffic demand is introduced, so that diverging flows can be easily computed with the supply–demand method. Then a Cell Transmission Model is proposed to solve the kinematic wave model of diverging traffic by taking into account of the interactions among different traffic streams. Simulation results demonstrate that vehicles follow the First-In-First-Out principle in the long run, and the model converges when we decrease the cell and time-step sizes. In addition, it is shown that traffic streams to different directions segregate in a selfish manner, and the total throughput of a diverging junction is not maximized as in existing diverge models. In the future, more theoretical and empirical studies are needed for a better understanding of this and other diverge models.