# Ring Road and Phantom Traffic Jams

The microscopic ring-road simulation scenario shows three-lane vehicular traffic in a closed system, symbolized by a ring road ("Indianopolis"). We simulate two types of vehicles, "cars" (small, color-coded by speed), and "trucks" (bigger and darker). The vehicle types are distinguished by the parameters of the Intelligent-Driver Model (IDM) which is a representative of the class of car-following models. For simplicity, we assume symmetric ("American") lane-changing and lane-usage rules, i.e., one can pass also on the right lane, and trucks can drive on the left lane whenever their drivers want to do it.

The dynamics depends essentially on the average vehicle density rho, which is the main control parameter in closed systems. In the simulations, you can vary the density. On increasing the density, new vehicles are "dropped at locations, where there is sufficiently space. On decreasing the density, arbitrarily selected vehicles are just removed. The following density ranges depend on the number and distibution of trucks and can vary from simulation to simulation.

- Density rho < 8 vehicles/km/lane: Free traffic. Only in very rare cases cars are blocked by two parallel-driving trucks.
- rho = 8..15 veh./km/lane: Queues of vehicles behind trucks become more frequently
- rho = 15..25 veh./km/lane: Traffic becomes so dense that, on average, also car-drivers drive more slowly than the maximum speed of trucks. Therefore, there are rarely distinct queues behind trucks. Traffic is dense, but yet without congestions.
- rho = 25..55 veh./km/lane: the initially nearly homogeneous traffic flow becomes unstable and small perturbations (caused by the trucks) develop to one or more "phantom" traffic jams emerging "out of nothing"! Notice that the stop-and go waves propagate against the driving direction.
- rho>50 veh./km/lane: Several regions with standing traffic separated by regions where vehicles move slowly.

## Feedback Mechanism for Traffic Jams

Assume that one car brakes a little bit (initial perturbation). As a consequence, the driver of the car behind has to brake as well to maintain the safety distance. Because the braking deceleration is finite, the gap between the two vehicle nevertheless becomes too low, and the driver of the car behind has to brake even more to regain the correct safety distance. As a consequence, the driver of the next vehicle behind has to brake even more and so on ... Besides this destabilizing mechanism, the relaxation to a certain gap-dependent local equilibrium velocity acts as a stabililizing mechanism. For sufficiently small (or very large) traffic densities, this latter effects is dominating and perturbations die out

## Universal properties of Traffic jams

Such stop-and go waves and other kinds of congested traffic have remarkably universal features characterized by the following "Traffic jam constants":

- The density waves propagate against the direction of the traffic flow at a velocity of about 15 km/h which does not depend on the system size, the initial or boundary conditions or on the perturbations
- For equal external conditions, the ouflow of all types of moving downstream fronts of congested traffic (per lane) is about the same. This includes stop-and-go waves (this scenario Ring Road and also the On-Ramp scenario) but also dissolving queues in city traffic when the traffic light gets green.