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

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.