Capacity drops at merges: Analytical expressions for multilane freeways

F Marczak, Ludovic Leclercq, Victor Knoop, Serge Hoogendoorn

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

7 Citations (Scopus)
18 Downloads (Pure)


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.
Original languageEnglish
Title of host publicationTransportation Research Board 95th annual meeting
Subtitle of host publicationWashington, United States
PublisherTransportation Research Board (TRB)
Publication statusPublished - 12 Jan 2016
EventTransportation Research Board 95th annual meeting - Washington, United States
Duration: 10 Jan 201614 Jan 2016
Conference number: 95


ConferenceTransportation Research Board 95th annual meeting
Abbreviated titleTRB 95
CountryUnited States


  • Freeways
  • Highway capacity
  • Lane changing
  • Mathematical analysis
  • Merging area
  • Multilane highways
  • Sensitivity analysis
  • traffic flow


Dive into the research topics of 'Capacity drops at merges: Analytical expressions for multilane freeways'. Together they form a unique fingerprint.
  • Greenshields Prize 2016

    Ludovic Leclercq (Recipient), F Marczak (Recipient), Knoop, V.L. (Recipient) & Hoogendoorn, S.P. (Recipient), 2016

    Prize: Prize (including medals and awards)

Cite this