Capacity drops at merges: New analytical investigations

• New analytical formulations are provided to determine the mean capacity drop value at freeway merges.
• Interactions between waves and voids influence the mean capacity drop value.
• Heterogeneous vehicle characteristics little influence the mean capacity drop value as far as mean parameters values are accurately calibrated.
• Heterogeneous vehicle characteristics have a strong influence on flow dynamics at merges.

This paper focuses on the derivation of analytical formulae to estimate the effective capacity at freeway merges. It extends previous works by proposing a generic framework able to account for (i) heterogeneous vehicle characteristics and (ii) refined description of the physical interactions between upstream waves and downstream voids created by inserting vehicles within the merge area. The provided analytical formulae permit to directly compute the capacity values when the merge is self-active, i.e. when both upstream roads are congested while downstream traffic conditions are free-flow. They show that accounting for vehicle heterogeneity is not necessary when only the mean capacity is targeted. Calculations with the proper mean value for all parameters provide almost the same results as calculations that consider the full distributions for all parameters. This means that calibrating all distributions is not necessary only the mean parameter values are important. Finally, this paper also shows that vehicle heterogeneity plays a major role in the flow dynamics just upstream of the merge.