Propagation of On-Ramp Density Waves on Uniform Unidirectional Multilane Freeways

This paper presents a generalized analysis of the effects of on-ramp time varying flow on unidirectional n-lane freeways. The analysis incorporates the speed-density relations for every lane, which are then used to set up separate continuity equations for every lane and are coupled by some reasonable lane-changing hypotheses. The paper assumes the same wave velocities (uniform freeway) for the perturbed flow in each lane of a freeway. Using the generalized n-lane analysis, the paper then predicts the relative propagation of density perturbations in time and space in different lanes of a two-lane, three-lane, and four-lane freeway. The corresponding relaxation distances from the on-ramp, where the initial perturbation had started, have been defined and compared for the two-lane, three-lane, and four-lane freeway. The above studies have then incorporated the effects of controlled ramp flow by suitable mathematical expressions that simulate controlled ramp flow.