Two-stage approximation allocation approach for real-time parking reservations considering stochastic requests and reusable resources

The digital economy has greatly impacted the traditional parking industry. This study focuses on a real-time parking reservation system that allocates available parking slots (supplies) to serve the parking requests (demands) of drivers within a certain area. The challenge lies in dealing with the randomness of requests with varying parking durations and the reusability of parking resources, which have not been well researched. To address this problem, we propose a stochastic optimization model and a data-driven two-stage approximation approach. The first stage generates a pre-allocation scheme as a basis, while the second stage dynamically adjusts the scheme based on observed requests and available parking slots to improve the system’s performance throughout a finite operational horizon. The study has three main contributions. Firstly, this paper proposes a data-driven nonparametric approach based on sample average approximation (SAA) to solve the stochastic optimization model. Secondly, it develops a stratified ranked set sampling (SRSS) method to ensure the quality of the sample set and proves that the sample set sampled by the SRSS method is unbiased. Finally, an evaluation method is proposed to establish a confidence interval for the expected revenue obtained by the data-driven method. Experimental results based on real parking demand data show that our approach outperforms both a commonly used heuristic allocation policy in the parking industry and the standard SAA approach with two popular sampling methods and an evaluation method based on Student’s T-test in the literature.