Optimal lane allocation strategy in toll stations for mixed human-driven and autonomous vehicles

Abstract

Highway toll stations are equipped with electronic toll collection (ETC) lanes and manual toll collection (MTC) lanes. It is anticipated that connected autonomous vehicles (CAVs), MTC human-driven vehicles (MTC-HVs), and ETC human-driven vehicles (ETC-HVs) will coexist for a long time, sharing toll station infrastructure. To fully leverage the congestion reduction potential of ETC, this paper addresses the problem of ETC lane allocation at toll stations under heterogeneous traffic flows, modeling it as a mixed-integer nonlinear bilevel programming problem (MINLBP). The objective is to minimize total toll station travel time by optimizing the number of ETC lanes at station entrances and exits while considering ETC-HVs’ lane selection behavior based on the user equilibrium principle. As both upper-level and lower-level problems are convex, the bilevel problem is transformed into an equivalent single-level optimization using the Karush–Kuhn–Tucker (KKT) conditions of the lower-level problem, and numerical solutions are obtained using the commercial solver Gurobi. Based on surveillance video data from the Liulin toll station (Lianhuo Expressway) in Zhengzhou, China, numerical experiments were conducted. The results illustrate that the proposed method reduces total vehicle travel time by 90.44% compared to the current lane allocation scheme or the proportional lane allocation method. Increasing the proportion of CAVs or ETC-HVs helps accommodate high traffic demand. Dynamically adjusting lane allocation in response to variations in traffic arrival rates is proven to be a more effective supply strategy than static allocation. Moreover, regarding the interesting conclusion that all ETC-HVs choose the ETC lanes, we derived the relaxed analytical solution of MINLBP using a parameter iteration method. The analytical solution confirmed the validity of the numerical experiment results. The findings of this study can effectively and conveniently guide lane allocation at highway toll stations to improve traffic efficiency.