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The design of dynamic tolling algorithms for managed lanes is complex and challenging, in part due to the often conflicting and differing objectives of the operator, travelers and the regulator. In this paper, we propose a framework for personalized pricing of managed lanes that combines elements of prediction, optimization, and personalization to dynamically determine displayed tolls and personalized discounts to travelers. The proposed approach involves an online bi-level optimization formulation consisting of coupled system-level and user-level optimization problems. The system optimization problem uses real-time traffic predictions (from a simulation-based dynamic traffic assignment model) to periodically determine displayed tolls and a discount control policy that maximize a multi-component system-level objective (considering different stakeholders with flexible policy hyperparameters). The user optimization problem consistently determines a personalized discount to offer to each individual traveler based on individual-specific preferences subject to the displayed toll and discount policy in effect. At the heart of both the system and user optimization problems is an individual-specific behavioral model (of choice between the managed lane and general purpose lanes) that incorporates state dependence (habit and loyalty formation), unobserved inter- and intra-consumer heterogeneity, and corrections for price endogeneity. Rigorous closed-loop simulations of an operational managed lane facility using real data demonstrate that the proposed personalized dynamic tolling approach improves operator revenue and managed lane usage, traveler benefits and equity, and reduces congestion relative to the existing tolling policy.
Xie et al. (Mon,) studied this question.