Optimal intersection design and signal setting in a transportation network with mixed HVs and CAVs

Abstract

It is widely recognized that human-driven vehicles (HVs) and connected and autonomous vehicles (CAVs) are expected to coexist and share the urban traffic infrastructure in the transportation network for a long time. To fully utilizes CAVs’ potential to reduce congestion in the transitional period, this study proposes and addresses the intersection design and signal setting problem in the transportation network with mixed HVs and CAVs. Due to the difference in terms of communication technology and autonomous driving technology for HVs and CAVs, three types of intersections have been proposed to amplify the efficiency-improvement benefit from CAVs by separating CAVs from HVs in a temporal or local-spatial dimension: the conventional signalized intersection, the novel signalized intersection with a dedicated CAV phase and dedicated CAV approaches, and the intelligent signal-free intersection. The problem is to determine the spatial layout of different types of intersections in the transportation network, the cycle time, and green time duration for each phase of signalized intersections that minimize the total travel cost, in which the route choice behavior of heterogeneous travelers has been respected based on the user equilibrium principle. A mixed-integer nonlinear programming model is developed to formulate the proposed intersection design and signal setting problem based on the link-node modeling method, in which the path enumeration is avoided. Then, by employing various linearization techniques (e.g., disjunctive constraints, logarithmic transformation, piecewise linearization with logarithmic-sized binary variables and constraints, outer-approximation technique), the proposed model can be further transformed into a relaxed sub-problem in the form of mixed-integer linear programming. A globally optimal solution algorithm embedding with solving a sequence of relaxed sub-problems and nonlinear mixed complementarity problems is proposed to converge to a global optimum. The results of numerical experiments illustrate that the proposed methodology can significantly improve the performance of the whole network. Moreover, it consistently outperforms the optimization model considering only conventional signalized intersections under various CAV market penetration rates.