Optimal roadside units location for path flow reconstruction in a connected vehicle environment

The path flow reconstruction problem is used to determine the minimum set of links that must be equipped with traffic monitoring devices to identify vehicle paths in a road network. This study addresses the path flow reconstruction problem in a connected vehicles (CVs) environment. Unlike traditional sensors that can observe both CVs and non-connected vehicles (NCVs), CV enabled infrastructures, known as roadside units (RSUs), can only identify CVs on roads through vehicle to infrastructure (V2I) communications. They can, however, provide critical traffic information, including traces of the historical trajectories of CVs and possibly the desired path to a destination, thereby inferring partial information on links that are not directly covered by RSUs. RSUs have an "area" rather than a "point" coverage capability. This allows them to simultaneously monitor more than one link. We mathematically developed four variant formulations for the path flow reconstruction problem to optimally locate either a network's RSU or a mix of the network's RSUs and automatic vehicle identification (AVI) sensors. The first two models assume 100% market penetration of CVs and the first model determines the links that should be directly covered by RSUs in a road network. While the desired path to a destination is assumed to be unknown. This model determines an upper bound for the number of RSUs required to fully reconstruct path flows by using each RSU to directly cover a link. To consider the coverage and range of the RSU (where RSU can cover more than one link) and to minimize the total cost, Model II optimizes the locations of traditional AVI sensors and RSUs. This allows the model to capitalize on the RSUs' area and indirect coverage features to fully reconstruct path flow in a road network. Model III considers the gradual deployment of CVs and thus the prevailing mixed traffic environment consisting of both CVs and NCVs. Accordingly, this model relaxes the assumption of a 100% penetration rate of CVs and maximizes the path flow information gain subject to a budget constraint in a mixed traffic environment. Finally, Model IV explores the infrastructure to infrastructure (I2I) communication capability among RSUs, further maximizing the traffic flow information gain of CVs while guaranteeing full path flow reconstruction. The results suggest that fewer RSUs than AVI sensors are required to reach full path flow reconstruction in a road network. The level of unique path flow information obtained from RSUs is also considerably higher than what can be obtained from AVI sensors. It is demonstrated that, in mixed traffic conditions, the coverage range of RSUs and their cost compared to AVI sensors can significantly affect the deployment of either type of sensing devices for maximized path flow information gain.