Communications - Scientific letters of the University of Zilina X:X | DOI: 10.26552/com.C.2026.054

Stopped Fraction and Closure Failure in Congested Macroscopic Fundamental Diagrams: A Sumo-Based Simulation Study

Tomoo Noguchi ORCID...
Waseda University, School of Social Sciences, Tokyo, Japan

Congested macroscopic fundamental diagrams (MFDs) often display scatter since accumulation alone does not fully describe immobilization within stored traffic. In this paper, the stopped fraction, defined as the share of vehicles that are stopped or nearly stopped, is examined as a complementary macroscopic state variable. A compact analytical framework shows why accumulation-only closure can fail when stopped fraction varies at fixed accumulation. The mechanism is tested using the Simulation of Urban MObility (SUMO) platform on a stylized signalized grid. Adding stopped fraction reduces the root mean squared error (RMSE) from 41.32 to 18.79 overall, and from 55.84 to 23.40 in the congested regime, where R² rises from 0.8777 to 0.9785. Stopped fraction therefore provides a practical diagnostic for congestion states omitted from accumulation-only MFD representations.

Keywords: macroscopic fundamental diagram, stopped fraction, SUMO simulation, congested traffic, closure failure, network production
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The author gratefully acknowledges helpful discussions from colleagues. Any remaining errors are solely the author’s responsibility.

Conflicts of interest:

The author declares that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Received: May 13, 2026; Accepted: September 2, 2026; Prepublished online: September 17, 2026 

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