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This paper aims to propose a new analytical method of deriving the enveloping macroscopic fundamental diagram (MFD) in the light of the well-defined sufficient condition and the route choice criterion in a general network. The enveloping MFD is defined to describe the boundary of all scatter points relating the flow rate (vehicles per unit time) to the vehicle accumulation (vehicles) in a road network. The theoretical framework consists of two parts. The first part is a static congested traffic assignment model which is based on the congested link performance function and the deterministic user equilibrium principle under the entirely congested condition. The second part is the new analytical method which is proposed based on the static uncongested and congested traffic assignments with the deterministic user equilibrium, in which the well-defined sufficient condition is satisfied by employing the static traffic assignment models, and the route choice criterion is fulfilled by the deterministic user equilibrium condition (Wardrop’s principle). The main findings of this paper are summarized as follows: 1) the enveloping MFD delimits a region where all scatter points are located; 2) the existence and reproducibility of the enveloping MFD in a general network are verified through numerical examples; 3) the proposed method is suggested to be applied to transportation planning for describing and evaluating the macro-characteristics and the performance of road networks and evaluating whether the OD pattern is congruous with the network topology.

Modeling the Enveloping Macroscopic Fundamental Diagram Based on the Traffic Assignment With Deterministic User Equilibrium