Numerical exploration of freeway tunnel effects with a two-lane traffic model

To explore freeway tunnel effects on ring road traffic flow, a two-lane traffic model is put forward. The model adopts lane-changing time to describe the net lane-changing rate, assuming that the time is approximately equal to the relaxation time of traffic flow, but infinite when the absolute value of difference of traffic density between the two lanes is lower than 1 veh/km, as it is hard for car drivers to perceive such a small difference. Based on the two-lane traffic model, a simulation platform is built to predict traffic flow on a two-lane freeway ring with a tunnel of 0.3 km length having a speed limit of 80 km/h, and free flow speeds on lane I and II equal to 120 and 100 km/h, respectively. The platform uses a third-order Runge–Kutta scheme to handle the time derivative term, and a fifth-order weighted essentially non-oscillatory scheme to calculate numerical flux. Simulation results show that the freeway tunnel can trigger traffic shock originating at the entrance when the coming flow density is beyond a traffic density threshold that is dependent on the off-ramp flow just upstream the tunnel. The occurrence of traffic shock leads to the mean travel time through the tunnel is almost a constant when the initial density normalized by jam density is less than 0.5. When initial density is above the density threshold, generally vehicles need more fuel consumption to run through the ring road in comparison with the case without tunnel. But the situation is just the opposite for larger normalized initial density such as 0.5.