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Application of a Discontinuous Form of Macroscopic Gazis–Herman–Rothery Model to Steady-State Freeway Traffic Stream Observations

In this study, a two-regime, steady-state, traffic stream model is developed by applying the macroscopic Gazis–Herman–Rothery model to fixed sensor data on freeways. The uncongested and congested regimes are modeled discontinuously with an overlap range defined in terms of density. The overlap is important as various phenomena related to the change in traffic state can be modeled by introducing this overlap. Two empirical tools for removing non-stationary, mixed-state, and erroneous observations are applied at different stages of the model development process. Three constraints justified by the Highway Capacity Manual (HCM) were applied to fit the model so that the fitted parameters have reasonable and physically interpretable values. The proposed model is applied to one year of data (2013) obtained from fixed sensors located at five freeway basic segments near Raleigh, North Carolina. The resulting fundamental diagrams show that the fitted models reasonably represent the steady-state observations. Two forms of the freeway flow model described in the HCM were applied to the same observations to provide a continuous model comparison. Two statistical performance measures, mean squared error of flow rate and Bayesian Information Criterion, verify that the proposed model is preferable to the HCM models both in terms of fit alone and when considering the tradeoff between fit and model complexity. It is expected that the proposed discontinuous steady-state model will be useful to researchers and practitioners to study various site-specific freeway traffic stream characteristics.