A kinematic wave theory of capacity drop

Wen-Long Jin, Qi-Jian Gan and Jean-Patrick Lebacque

Transportation Research Part B: Methodological, 2015, vol. 81, issue P1, 316-329

Abstract: Capacity drop at active bottlenecks is one of the most puzzling traffic phenomena, but a thorough understanding of its mechanism is critical for designing variable speed limit and ramp metering strategies. In this study, within the framework of the kinematic wave theory, we propose a simple model of capacity drop based on the observation that capacity drop occurs when an upstream queue forms at an active bottleneck. Different from existing models, the new model still uses continuous fundamental diagrams but employs an entropy condition defined by a discontinuous boundary flux function, which introduces a traffic state-dependent capacity constraint. For a lane-drop area, we demonstrate that the model is well-defined, and its Riemann problem can be uniquely solved. After deriving the flow-density relations upstream and downstream to a bottleneck location, we find that the model can replicate the following three characteristics of capacity drop: the maximum discharge flow-rate can be reached only when both upstream and downstream traffic conditions are uncongested, capacity drop occurs when the bottleneck is activated, and some steady traffic states cannot be observed at both locations. We show that the new model is bistable subject to perturbations in initial and boundary conditions. With empirical observations at a merging bottleneck we also verify the three characteristics of capacity drop predicted by the new model. Through this study, we establish that the new model is physically meaningful, conceptually simple, computationally efficient, and mathematically tractable. We finally discuss future extensions and potential applications of the new model.

Keywords: Capacity drop characteristics; Kinematic wave theory; Continuous fundamental diagram; Discontinuous entropy condition; Riemann problem; Stability (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0191261515001678
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:81:y:2015:i:p1:p:316-329

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.trb.2015.07.020

Access Statistics for this article

Transportation Research Part B: Methodological is currently edited by Fred Mannering

More articles in Transportation Research Part B: Methodological from Elsevier
Bibliographic data for series maintained by Catherine Liu ().