A Differentially Private Incentive Design for Traffic Offload to Public Transportation

Abstract

Increasingly large trip demands have strained urban transportation capacity, which consequently leads to traffic congestion and rapid growth of greenhouse gas emissions. In this work, we focus on achieving sustainable transportation by incentivizing passengers to switch from private cars to public transport. We address the following challenges. First, the passengers incur inconvenience costs when changing their transit behaviors due to delay and discomfort, and thus need to be reimbursed. Second, the inconvenience cost, however, is unknown to the government when choosing the incentives. Furthermore, changing transit behaviors raises privacy concerns from passengers. An adversary could infer personal information (e.g., daily routine, region of interest, and wealth) by observing the decisions made by the government, which are known to the public. We adopt the concept of differential privacy and propose privacy-preserving incentive designs under two settings, denoted as two-way communication and one-way communication. Under two-way communication, passengers submit bids and then the government determines the incentives, whereas in one-way communication, the government simply sets a price without acquiring information from the passengers. We formulate the problem under two-way communication as a mixed integer linear program and propose a polynomial-time approximation algorithm. We show the proposed approach achieves truthfulness, individual rationality, social optimality, and differential privacy. Under one-way communication, we focus on how the government should design the incentives without revealing passengers’ inconvenience costs while still preserving differential privacy. We formulate the problem as a convex program and propose a differentially private and near-optimal solution algorithm. A numerical case study using the Caltrans Performance Measurement System (PeMS) data source is presented as evaluation. The results show that the proposed approaches achieve a win-win situation in which both the government and passengers obtain non-negative utilities.