Macroscopic Traffic Flow Analysis and Optimization with V2I Connectivity and Collision Avoidance Constraints

In fully automated traffic streams, speed optimization of connected and autonomous vehicles (CAVs) is a fundamental challenge. However, while increasing the CAVs' speed improves traffic flow, it increases communication handoffs as the CAVs switch from one base station (BS) to another, thus reducing communication data rates. Therefore, a trade-off exists between the communication data rates and CAV traffic flow. In this paper, we develop a novel framework to analyze and maximize the macroscopic traffic flow by optimizing the speed of CAVs and network deployment such that the CAVs' data rate requirements can be satisfied. We first characterize a closed form expression of the macroscopic traffic flow by considering exponential distribution of the spacing between CAVs. The derived expression is used to jointly optimize the deployment of BSs and speed of CAVs while maximizing the CAVs' traffic flow with collision avoidance and handoff-aware data rate constraints. Closed-form optimal solutions are then presented for the CAV's speed and the number of BSs deployed along the corridor considering a high signal-to-noise ratio (SNR) regime. Numerical results validate the accuracy of the derived expressions. Our results show that increasing the BS density or lowering the data rate requirements of CAVs enhances the data rates which increases CAV speeds and in turn the traffic flow.