On- and Off-ramps Generating 1/f Noise in Traffic Flow

Abstract

A simple model of a motorway junction consisting of two connected periodic roads is presented; each of them is connected to the other by on- and off-ramps. This constitutes a detailed structure for the region of on- and off-ramps, which is a new aspect of this paper and a useful step towards a more realistic modelling of the vehicular dynamics near the ramps. The traffic flow through the ramps has an effect on the capacity of the main roads. This effect is identified by the formation of the so-called ”plateau” in the fundamental diagram. The value increase of one of the probabilities pin and pout decreases the value of the indicated plateau. Here pin is the probability to enter the main road through the on-ramp and pout denotes the probability to exit the main road through the off-ramp. The first important feature in the simulated system is the symmetry between the connected main roads. This symmetry does not depend on the variation of the difference between the probabilities pin and pout. The other most outstanding feature is the existence of correlations between the connected main roads, which can be traced back to the lane change of vehicles in the ramp regions. These correlations are characterized by the occurrence of 1/f^α fluctuations in the global traffic flow of a chosen main road of the simulated system.