基于马尔可夫模型的大规模交通流分析与仿真
Large-scale Analysis and Simulation of Traffic Flow using Markov Models
摘要：
在已建立的交通基础设施中，特别是在大型城市道路网络中，对车辆运动进行建模和仿真是一项重要的任务。它有助于理解和处理交通问题，优化交通规则，并实时调整交通管理以应对突发灾难事件。一个数学上严格的随机模型，可用于交通分析，提出了较早的其他研究人员，这是基于图和马尔可夫链理论之间的相互作用。该模型提供了一个转移概率矩阵，它描述了交通的动态与其唯一的静态分布的车辆在道路网络。本文通过引入二维平稳分布的概念，提出了一种新的参数化方法，该方法可以同时处理交通流的动态特性和车辆的分布特性。此外，加权最小二乘估计方法被应用于估计新的参数矩阵，使用轨迹数据。在一个案例研究中，我们将我们的方法应用于出租车轨迹预测数据集和OpenStreetMap项目的道路网络数据，两者都是公开的。为了测试我们的方法，我们在软件中实现了所提出的模型。我们已经在中、大尺度上进行了模拟，基于人工和真实数据集的模型和估计过程都被证明是令人满意的。在一个实际应用中，我们基于数据集在波尔图的地图图上展开了一个静态分布。这里描述的方法结合了技术，其一起使用，以分析大型道路网络上的交通以前没有报道。
英文摘要：
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic regulations and adapting the traffic management in real time for unexpected disaster events. A mathematically rigorous stochastic model that can be used for traffic analysis was proposed earlier by other researchers which is based on an interplay between graph and Markov chain theories. This model provides a transition probability matrix which describes the traffic's dynamic with its unique stationary distribution of the vehicles on the road network. In this paper, a new parametrization is presented for this model by introducing the concept of two-dimensional stationary distribution which can handle the traffic's dynamic together with the vehicles' distribution. In addition, the weighted least squares estimation method is applied for estimating this new parameter matrix using trajectory data. In a case study, we apply our method on the Taxi Trajectory Prediction dataset and road network data from the OpenStreetMap project, both available publicly. To test our approach, we have implemented the proposed model in software. We have run simulations in medium and large scales and both the model and estimation procedure, based on artificial and real datasets, have been proved satisfactory. In a real application, we have unfolded a stationary distribution on the map graph of Porto, based on the dataset. The approach described here combines techniques whose use together to analyze traffic on large road networks has not previously been reported.
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