A multiclass link transmission model for dynamic network loading of mixed legacy and automated vehicle flow

Abstract

As automated vehicles gradually become available to travelers, many cities will experience a mixed traffic flow consisting of both legacy and automated vehicles. Although the overall market penetration of automated vehicles may be known, the proportion of automated vehicles may vary in space and time due to spatial and temporal variations in automated vehicle demand. Since automated vehicles are expected to behave differently than legacy vehicles, this results in a flow-density relationship that varies in both time and space with the local proportion of automated vehicles. We model this scenario using a multiclass kinematic wave theory. Assuming a triangular flow-density relationship (with shape parameters varying with the automated vehicle proportion), we develop a multiclass Newell's method for finding exact solutions to the multiclass kinematic wave theory. The solution method takes the form of a linear program with postprocessing. We then extend this method to a multiclass link transmission model. We develop a faster solution method for the receiving flow which consists of iteratively solving a system of linear equations. Numerical results from dynamic traffic assignment on the downtown Austin city network demonstrate the computational tractability of this method and explore the effects of automated vehicles on traffic congestion.