In this paper, two types of parking spaces, namely public and private parking spaces, are technically allocated to the drivers who may require a long or short time slot. Dynamic allocation and pricing process increase the complexity of evaluating the performance. We design a Physical Internet (PI) enabled parking management system to establish parking networks and collect real-time information for management and evaluation. Then, we propose a truthful, reverse Vickrey auction to allocate and price parking spaces in a static setting. We further incorporate the static auction mechanism into a continuous-time Markov Chain model and analyze the effects of the key factors (e.g., dynamic arrival rate and abandonment rate) in a dynamic setting. Our experimental results show that the expected price of the reverse Vickrey auction is lower than the market price. The expected profit is increasing in the arrival rate of parking spaces in the system. Finally, we numerically examine the benefits of parking space owners, drivers and the system, and highlight the associated managerial implications.

本文将两种类型的停车位，即公共和私人停车位，从技术上分配给可能需要较长或较短时间段的驾驶员。动态分配和定价过程会增加评估绩效的复杂性。我们设计了一个基于物理Internet（PI）的停车管理系统，以建立停车网络并收集实时信息以进行管理和评估。然后，我们提出了一个真实的，反向的Vickrey拍卖，以在静态环境中分配和定价停车位。我们将静态拍卖机制进一步纳入了连续时间马尔可夫链模型，并在动态环境中分析了关键因素（例如，动态到达率和放弃率）的影响。我们的实验结果表明，反向Vickrey拍卖的预期价格低于市场价格。预期利润会增加系统中停车位的到达率。最后，我们从数字上检查了停车位所有者，驾驶员和系统的好处，并强调了相关的管理含义。