Simple model for urban traffic between two signalized intersections

This paper introduces a new model of traffic flow between two signalized intersections. The model originated from our effort to improve older, macroscopic model [5] based on the conservation law of vehicles. In order to keep the proposed model simple and numerically tractable, we make several simplifications: we do not take into account acceleration and deceleration of vehicles and different preferences of drivers and we classify the movements of vehicles into two classes: (i) a stopped vehicle, waiting in a queue, and (ii) a vehicle moving with a constant cruising speed. Under these assumptions the flow of vehicles between two intersections can be described by a piece-wise linear function as a combination of several "ramp" functions. We demonstrate the behavior of the proposed model on an simulated scenario of two signalized intersections.