Traffic systems are multi-agent cyber-physical systems whose performance is closely related to human welfare. They work in open environments and are subject to uncertainties from various sources, making their performance hard to verify by traditional model-based approaches. Alternatively, statistical model checking (SMC) can verify their performance by sequentially drawing sample data until the correctness of a performance specification can be inferred with desired statistical accuracy. This work aims to verify traffic systems with privacy, motivated by the fact that the data used may include personal information (e.g., daily itinerary) and get leaked unintendedly by observing the execution of the SMC algorithm. To formally capture data privacy in SMC, we introduce the concept of expected differential privacy (EDP), which constrains how much the algorithm execution can change in the expectation sense when data change. Accordingly, we introduce an exponential randomization mechanism for the SMC algorithm to achieve the EDP. Our case study on traffic intersections by Vissim simulation shows the high accuracy of SMC in traffic model verification without significantly sacrificing computing efficiency. The case study also shows EDP successfully bounding the algorithm outputs to guarantee privacy.

翻译：交通系统是多智能体信息物理系统，其性能与人类福祉密切相关。这些系统在开放环境中运行，面临来自多种来源的不确定性，使得传统基于模型的方法难以验证其性能。因此，统计模型检验（Statistical Model Checking, SMC）通过顺序采集样本数据，直到能以所需统计精度推断性能规范的正确性，从而验证系统性能。本研究旨在验证具有隐私保护的交通系统，其动机在于所使用的数据可能包含个人信息（如日常行程），且通过观察SMC算法的执行可能无意中泄露这些信息。为在SMC中形式化捕捉数据隐私，我们引入了期望差分隐私（Expected Differential Privacy, EDP）概念，该概念限制了数据变化时算法执行在期望意义上的变化程度。相应地，我们为SMC算法引入了一种指数随机化机制以实现EDP。通过Vissim仿真对交通路口进行的案例研究表明，SMC在交通模型验证中具有高精度，且不会显著牺牲计算效率。该案例还表明，EDP成功限制了算法输出以确保隐私保护。