Estimating key traffic state parameters through parsimonious spatial queue models

As an active performance evaluation method, the fluid-based queueing model plays an important role in traffic flow modeling and traffic state estimation problems. A critical challenge in the application of traffic state estimation is how to utilize heterogeneous data sources in identifying key interpretable model parameters of freeway bottlenecks, such as queue discharge rates, system-level bottleneck-oriented arrival rates, and congestion duration. Inspired by Newell's deterministic fluid approximation model, this paper proposes a spatial queue model for oversaturated traffic systems with time-dependent arrival rates. The oversaturated system dynamics can be described by parsimonious analytical formulations based on polynomial functional approximation for virtual arrival flow rates. With available flow, density and end-to-end travel time data along traffic bottlenecks, the proposed modeling framework for estimating the key traffic queueing state parameters is able to systematically map various measurements to the bottleneck-level dynamics and queue evolution process. The effectiveness of the developed method is demonstrated based on three case studies with empirical data in different metropolitan areas, including New York, Los Angeles, and Beijing.