Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks

Igor Kuverin; Sergey Gusev; Vladimir Marosin

doi:10.20295/2412-9186-2026-12-03-217-227

UDC 656.13 UDC 007.52

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MACROSCOPIC FUNDAMENTAL DIAGRAM IN THE MAXIMUM FLOW PROBLEM FOR SELF‑DRIVING TRANSPORT NETWORKS Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks

АА Аа

Published in Transport automation research · Volume 12, Issue 3, 2026 · Pages 217–227 · Rubric: INTELLIGENT CONTROL SYSTEMS

DOI: https://doi.org/10.20295/2412-9186-2026-12-03-217-227

Received: 17.09.2026 Accepted: 19.09.2026 Published: 19.09.2026

Authors

Igor Kuverin

Sergey Gusev

Vladimir Marosin

Igor Kuverin

Academic degree: candidate of technical sciences

Yuri Gagarin State Technical University of Saratov Associate Professor · Department of “Organization of transportation, traffic safety and car service” · Russian Federation · Saratov

Sergey Gusev

Academic degree: doctor of economic sciences

Science rang: professor

Yuri Gagarin State Technical University of Saratov Head of Department · Department "Organization transportation, traffic safety and car service" · Russian Federation · Saratov

Vladimir Marosin

Diall Alliance LLC Specialist in Management and Configuration of Regulatory and Reference Information · Russian Federation

ABSTRACT

the transition to the widespread use of unmanned vehicles as part of intelligent transport systems creates an unprecedented opportunity for centralized, coordinated management of traffic flows. Unlike traditional traffic, where decisions are made by multiple independent drivers, connected unmanned vehicles can act as the operational elements of a network controller. The article proposes an analytical model that combines the classic Ford — Fulkerson maximum flow problem with a macroscopic fundamental diagram that takes into account the nonlinear reduction in the capacity of road network nodes under overload conditions. The model is formulated as a nonlinear network programming problem, where the flow of unmanned vehicles is managed in such a way as to prevent the occurrence of congestion states in network zones described by a macroscopic fundamental diagram. An iterative algorithm has been developed that generalizes the complementary path method: at each step, the residual capacity is adjusted taking into account the current saturation, and the presence of backward arcs allows for the real-time “recall” of the unmanned vehicle flow from zones approaching critical accumulation. A criterion of optimality has been obtained, stating that the flow is maximal if and only if it is impossible to find a route connecting the source to the sink in the residual network constructed taking into account the constraints of the macroscopic fundamental diagram. It has been shown that the model can serve as a reference computational core for the upperlevel routing subsystem of an intelligent transport network, ensuring the prevention of network congestion and the maximization of the road network’s throughput capacity.

KEYWORDS

intelligent transport system, autonomous vehicles, maximum flow, Ford — Fulkerson algorithm, macroscopic fundamental diagram, Macroscopic Fundamental Diagram, nonlinear constraints, residual network, network control

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GOST

Kuverin I. Y., Gusev S. A., Marosin V. S. Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks // Transport automation research. 2026. no. 3. pp. 217-227. DOI: https://doi.org/10.20295/2412-9186-2026-12-03-217-227. (Date of access 03.11.2026).

MLA

Igor Kuverin, Gusev S. A., Marosin V. S.. "Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks." Transport automation research 12.3 (2026): 217-227. DOI: https://doi.org/10.20295/2412-9186-2026-12-03-217-227.

APA

Kuverin I. Y., Gusev S. A., Marosin V. S. (2026). Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks. Transport automation research, 12(3), 217-227. https://doi.org/10.20295/2412-9186-2026-12-03-217-227

Chicago

Igor Kuverin, Gusev S. A., Marosin V. S.. "Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks." Transport automation research 12, no. 3 (2026): 217-227. https://doi.org/10.20295/2412-9186-2026-12-03-217-227.

WIKI

{{cite journal | author = Kuverin I. Y., Gusev S. A., Marosin V. S. | title = Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks | journal = Transport automation research | year = 2026 | volume = 12 | issue = 3 | pages = 217-227 | doi = 10.20295/2412-9186-2026-12-03-217-227 }}

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MACROSCOPIC FUNDAMENTAL DIAGRAM IN THE MAXIMUM FLOW PROBLEM FOR SELF‑DRIVING TRANSPORT NETWORKS Macroscopic Fundamental Diagram in the Maximum Flow Problem for Self‑Driving Transport Networks

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