The Spatial Evolution of Traffic Under the Two Wave Speed Assumption: A Shortcut Procedure and Some Observations

This paper describes the behavior of traffic in a homogeneous highway according to the hydrodynamic theory, in the special casewhere the flow-density relationship is triangular; i.e. when only two wave velocities exist. It presents an exact formula thatpredicts the vehicle that would be found at position x at time t, given the locations of all the vehicles at time zero. The formula, which does not require identification of the vehicle positions at intermediate times, automatically accounts for the creation and dissipation of any shocks. It can be used to calculate system performance measures such as the flow, speed and density at any future point in time-space and the vehicle travel times. The paper also introduces two graphical procedures. The first one identifies all the vehicle positions along the highway for any fixed t, and the second one identifies the traffic state on all the points in time-space. The second procedure can also be applied to highways that are in homogeneous in space (e.g. including lane drops) and/or time (e.g. including traffic lights), if.suitable boundary conditions between adjoining homogeneous sections can beidentified. An example involving a moving lane drop, as would occur behind a snow plow, is given.