Framework for Deriving Macroscopic Demand Functions from Microscopic Acceleration Models

Abstract

Vehicle acceleration plays an integral role in determining the operational capacity of roadway sections. Traditional first-order macroscopic models of traffic do not capture the boundedness of vehicle acceleration. In a recent study, it was shown that the cell transmission model could capture critical macroscopic effects of bounded acceleration if one modified the demand function such that traffic demand (sending flow) decreased in density for congested traffic. However, such a modified demand function was calibrated only with data. This paper introduces a framework for deriving such macroscopic demand functions corresponding to well-known microscopic acceleration models. Two mechanisms are explored for deriving the demand function with varying assumptions on how vehicles accelerate within a single discretized cell. The first mechanism is based on the assumption that vehicles within a single cell begin accelerating at the same time and that this information of the trigger of acceleration propagates instantaneously. The second mechanism assumes that the information for the trigger propagates within the cell at a finite speed such that following vehicles begin their acceleration process later than the leading vehicles. The derived demand functions are consistent with those calibrated with data. This study explicitly bridges macroscopic and microscopic models of bounded acceleration and can lead to more efficient evaluation of the effects of bounded acceleration on traffic systems.