Combined Effect of the Go-notGo Signal and a Bottleneck on the High-Speed Traffic Flow

The effect of the Go-notGo signal, which controls the start of every car, on the flow of cars in a one-dimensional highway with a bottleneck (a gate) is studied for the Fukui–Ishibashi model, where the maximum speed assigned to cars is set to M. Through macroscopic analyses, the car density pj in the jam flow part formed before the gate is found to play a key role, and by using pj expressed in terms of the probability f that cars are prohibited to move and the probability r of the gate acting as the bottleneck being open, a formula for the constant flow FC is obtained at an intermediate car density. Computer simulations for the M = 2 case were performed to test the validity of the obtained formula. It turned out that the formula reproduces the simulation results fairly well for the entire range of f and r.