Network throughput under dynamic user equilibrium: Queue spillback, paradox and traffic control

Abstract This study aims to analyze the relationship between a macroscopic fundamental diagram (MFD), which relates vehicle accumulation with throughput at the network level, and the spatial distribution of congestion (congestion pattern) in a general network with one-to-many origin-destination demands. In particular, we clarify the causes of a decreasing branch of MFDs and the influence of local signal controls on the (global) network throughput. For this aim, we present a new inverse problem of the dynamic user equilibrium assignment by using a periodic boundary condition, and an analytical formula of the network throughput for a fixed accumulation is derived by solving it. This enables us to incorporate the effects of network configurations and route choice behaviors into the analysis of the network throughput. By conducting a sensitivity analysis of this formula, we identify the types of congestion patterns that cause the decrease in the network throughput and examine a network signal control for improving network performance.