Symmetries in the kinematic wave model and a parameter-free representation of traffic flow

• The family of linear transformations where conservation laws are invariant is identified.
• For a subset of these transformations, flow, total distance traveled and total delay are invariant.
• This means that for capacity or delay computations one may choose the shape of the triangular fundamental that simplifies the problem the most.
• Delay-optimizing control problems may be solved using an isosceles fundamental diagram, which provides the most efficient numerical methods.

This paper identifies a family of linear transformations where conservation laws are invariant. In the case of a triangular fundamental diagram, it is shown that for a subset of these transformations, flow, total distance traveled and total delay are invariant. This means that for capacity or delay computations one may choose the transformation—i.e., the shape of the triangular diagram—that simplifies the problem the most, which does not require knowing the actual fundamental diagram. This is appealing also for delay-optimizing control problems since they may be solved using an isosceles fundamental diagram, which provides the most efficient numerical methods. Examples are given.