Boundary Conditions

Depending on the simulation scenario, we use periodic and open boundary conditions.

Periodic Boundary Conditions

These apply to the ring-road scenario. These conditions are easy:

Open Boundary Conditions

These conditions are more tricky. Specifically, one has to distinguish between outflow and inflow boundary conditions.

Outflow Boundary Conditions

Here, we assume just a free road, i.e., the gap of the first vehicle of the simulation is just set to infinity, so this vehicle accelerates freely until it is taken out of the simulation once it crosses the end of the simulated road section.

Inflow Boundary Conditions

These are the most tricky ones since the requested inflow cannot always be accomodated by the road, particularly if high inflows are set by the sliders, or a traffic jam or stop-and-go wave propagates to the upstream end. In the simulator, we do the following: This makes sure that the requested inflow is accepted whenever this is possible, and no crashes occur otherwise, i.e., when the upstream end of the road is congested and/or the demand is too high.
Martin Treiber