A fundamental diagram-consistent fluid queue model for dynamic throughput under heavy traffic congestion

AbstractThe efficient operation of transportation systems is a critical priority for policymakers, particularly given the increasingly emphasis on efficiency gains to meet growing travel demands without relying solely on capacity expansion. During peak hours at freeway bottleneck locations, a flow drop may be observed, and this drop is influenced by traffic stream attributes such as merging and diverging vehicles, resulting in significant efficiency losses. However, queue-based models, widely used for estimating delays and queue lengths, often oversimplify congestion dynamics by assuming a constant outflow rate, leading to inconsistencies when compared with FD-based observations of over-congested states. In this manuscript, we introduce a novel Fundamental Diagram-Consistent Fluid Queue (FDQ) framework for analyzing and mitigating traffic efficiency losses during heavy congestion. We extend the traditional fluid queue model by incorporating a stationary density-flow relationship observed empirically at key bottlenecks. Unlike classical queue-based models, our framework allows the flow throughput to evolve with local traffic state transitions, especially the shift from semi-congested to fully congested regimes. We start with triangular FD and show how to analytically derive FD-consistent dynamic flow throughput, as well as the associated traffic states such as the queue profile and waiting time. Such framework is then utilized to understand efficiency loss mechanisms and explore the potential for increased system efficiency through targeted inflow control. Two types of FDQ models were developed: one with flow throughput in polynomial form (FDQ-PN) and another in piecewise form (FDQ-PW). The FDQ framework is also extended to work with quadratic FD. Validation and numerical analyses were performed using datasets from Los Angeles I-405 and Phoenix I-10. The results demonstrate that the proposed framework substantially improves the accuracy of traffic state estimation. Furthermore, the demand–supply coupled inflow control is shown to offer a more significant efficiency gain than adjusting demand or supply alone.