Optimal policy for integrating Autonomous Vehicles into the auto market

Abstract

With the advent of emerging technologies, autonomous vehicles (AVs) are expected to become increasingly available to travelers. It is highly anticipated that there will be a transitional period when legacy vehicles (LVs) are gradually replaced by AVs before AVs take up a full penetration in the auto market. As a result, LVs and AVs will inevitably coexist during this period experiencing an interactive temporal evolution in terms of their market shares. Inspired by the classic Lotka–Volterra equations, we develop a continuous-time dynamical model capable of capturing such temporal evolution. A discrete choice model is constructed and incorporated into the dynamical model for describing the likelihood of choosing LVs or AVs. To achieve the desired temporal integration of AVs, monetary subsidies and investment in AV-specific transportation infrastructure are considered as decision variables to promote the adoption of AVs. Further, an optimal control problem is formulated with the objective of achieving a desired market penetration rate (MPR) of AVs at the end of the planning horizon, while minimizing the cost associated with AV subsidies and infrastructure investment. We prove the existence of an optimal AV integration policy. Moreover, we derive necessary conditions of optimality characterizing the mathematical properties of the optimal integration policy. Based on the optimality conditions derived, an iterative computational algorithm is developed to determine the time-dependent integration policy, which allows the government agency to appropriately subsidize AV purchases and invest in AV-specific infrastructure in an adaptive manner. Extensive numerical results are presented to show the effectiveness and robustness of the proposed approach under two distinct demand patterns. In addition, a systematic cost–benefit analysis is conducted, along with appropriate sensitivity analysis, to evaluate the desirability of the integration of AVs. Since the dynamical model is general and the decision variables are easy to implement, the procedures presented in this article will provide significant managerial insights for government agencies into developing long-term strategic planning policies.