Empirical observations of capacity drop in freeway merges with ramp control and integration in a first-order model

An accurate density monitoring along a stretch of a freeway, especially under congested time-variant conditions is necessary to evaluate congestion levels, understand complex traffic phenomena and develop efficient control strategies. In the first part of the paper (i) we show empirical evidence from freeway-ramp merges in Twin Cities freeway system, in favor of the capacity drop phenomenon, (ii) we provide a methodology based on phase diagrams to quantitatively estimate the level of the drop, (iii) we show that the level of the drop depends on the ratio of mainline vs. ramp flow and (iv) we investigate whether implementation of control strategies has an effect on the value of capacity drop. In the second part of the paper, we develop a methodology to estimate densities with space and time based on data from loop detectors, by integrating the capacity drop. The methodology is based on solving a flow conservation differential equation (using LWR theory) with intermediate (internal) freeway mainline boundaries, which is faster and more accurate from approaches using only external boundaries. To capture the capacity drop phenomenon into the first-order model we utilize a fundamental diagram with two values of capacity and we provide a memory-based methodology to choose the appropriate value in the numerical solution of the problem with a Godunov scheme. Results compared with real data and micro-simulation of a long freeway stretch show that this model produces more reliable and accurate results than previous theories.