Privacy-Preserving Estimation of $k$ -Persistent Traffic in Vehicular Cyber-Physical Systems

Traffic volume estimation is critical to the intelligent transportation engineering. Previous state-of-the-art studies mainly focus on measuring two types of traffic volume: “point” traffic (i.e., the number of vehicles passing a given location) and “point-to-point” traffic (i.e., the number of vehicles traversing between two given locations) during each measurement period. In this paper, we extend this line of research from single-period to multiple periods and study new problems of estimating the number of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-persistent vehicles that pass a location or two different locations in at least <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> predefined measurement periods. We propose two novel <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-persistent traffic estimators with privacy-preserving for the point and point-to-point traffic models, respectively. Through theoretical analysis, we prove that our solution can solve more general traffic measurement problems and employ stronger privacy preserving, i.e., <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-differential privacy, than the existing studies. We also demonstrate the effectiveness and the accuracy of the proposed estimators through extensive experiments based on real transportation traffic flows in Shenzhen, China for five consecutive working days. The numerical results show that the estimators can achieve a tradeoff between the estimation accuracy and privacy preservation through proper parameter setting.