Capacity Drops at Merges: Analytical Expressions for Multilane Freeways

This paper deals with the derivation of analytical formulas to estimate the effective capacity at freeway merges in a multilane context. The paper extends the findings presented in two previous papers describing studies that were based on the same modeling framework but that were restricted to a single lane on the freeway (or to the analysis of the right lane only). The analytical expression for the one-lane capacity was recursively applied to all lanes. Lane-changing maneuvers (mandatory for the on-ramp vehicles and discretionary for the other vehicles) were divided into two nonoverlapping local merging areas. Discretionary lane changes were transformed into a lane-changing flow by the use of appropriate analytical formulas. These formulas defined a system of equations whose unknowns were the capacity on all lanes and the inserting flow coming from the on-ramp. A sensitivity analysis showed that vehicle acceleration and the truck ratio were the parameters that most influenced the total capacity. The results obtained with the analytical formulas were proven to match the numerical results obtained from a traffic simulator that fully describes vehicle dynamics. Finally, the results provide good estimates in comparison with experimental data for an active merge on the M6 Motorway in the United Kingdom.