Capacity drops at merges: Analytical expressions for multilane freeways

This paper deals with the derivation of analytical formulae to estimate the effective capacity at freeway merges in a multilane context. It extends two previous papers that are based on the same modeling framework but that are 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 is recursively applied for all lanes. Lane-changing maneuvers (mandatory for the on-ramp vehicles and discretionary for others) are divided into two non-overlapping local merging areas. Discretionary lane-changes are transformed into a lane-changing flow using an appropriate analytical formula. This defines a system of equations whose unknowns are the capacity on all lanes and the inserting flow coming from the on-ramp. A sensitivity analysis shows that vehicle acceleration and the truck ratio are the most influential parameters for the total capacity. The analytical formulae are proven to match with numerical results from a traffic simulator that fully describes vehicle dynamics. Finally, they provide very good estimates when compared to experimental data for an active merge on the M6 freeway in UK.