The increase in traffic in cities world-wide has led to a need for better traffic management systems in urban networks. Despite the advances in technology for traffic data collection, the collected data are still suffering from significant issues, such as missing data, hence the need for data imputation methods. This paper explores the spatiotemporal probabilistic principal component analysis (PPCA) based data imputation method that utilizes traffic flow data from vehicle detectors and focuses specifically on detectors in urban networks as opposed to a freeway setting. In the urban context, detectors are in a complex network, separated by traffic lights, measuring different flow directions on different types of roads. Different constructions of a spatial network are compared, from a single detector to a neighborhood and a city-wide network. Experiments are conducted on data from 285 detectors in the urban network of Surabaya, Indonesia, with a case study on the Diponegoro neighborhood. Methods are tested against both point-wise and interval-wise missing data in various scenarios. Results show that a spatial network adds robustness to the system and the choice of the subset has an impact on the imputation error. Compared to a single detector, spatiotemporal PPCA is better suited for interval-wise errors and more robust against outliers and extreme missing data. Even in the case where an entire day of data is missing, the method is still able to impute data accurately relying on other vehicle detectors in the network.

The growth of vehicle mobility in the past decades and increased traffic complexity leads to a need for traffic management systems, especially in large-scale urban traffic networks. The erroneous data problems are common problems that affect traffic management systems. The traffic management systems also relied on traffic prediction particularly in traffic signal control and route guidance. This paper investigated probabilistic principal component analysis (PPCA) methods to impute missing traffic count data and predict future data. We also investigated the resulting principal components' significance in urban traffic analysis. These methods are applied to traffic count data from vehicle detectors in the urban network of Surabaya city, Indonesia. The results show that the PPCA-based data imputation method is able to impute missing data with imputation error under 20% WMAPE. The resulting principal components analysis demonstrates that 1 ^st principal component scores can be seen as a fundamental temporal pattern of the Surabaya urban network while the characteristic of the link can be derived from the 1 ^st principal component coefficient. We also demonstrate that 1 ^st principal component coefficient of the link might detect outliers or anomalies such as detector malfunction and unique temporal pattern. PPCA can also be used to predict future data based on observed data, but experiments show that even though the majority of the links can be predicted accurately, some links are having large errors that might be caused by different temporal patterns between future data and observed data.

Traffic flow prediction, crucial for traffic management, relies on spatial and temporal data to achieve high accuracy. However, standard performance metrics only measure the average prediction errors and overlook the spatiotemporal aspects. To address this gap, this study introduces three simple spatial key performance indicators (KPIs): Global Moran’s I, Getis-Ord General G, and Adapted PageRank Algorithm Modified (APAM). We evaluated the traffic prediction results for synthetic clustering scenarios and four different prediction methods applied to the PeMSD8 dataset using spatial KPIs. Spatial KPIs are calculated based on traffic prediction errors and the adjacency matrix of the traffic network. Our results demonstrate that spatial KPIs can effectively differentiate between synthetic clustering scenarios. Global Moran’s I measures the spatial autocorrelation, Getis-Ord General G measures the spatial clustering of high/low values, and the univariate analysis of APAM deduces the distribution of node importance by considering node centrality and node values. Getis-Ord General G showed the highest sensitivity, being capable of distinguishing between methods with similar average RMSE, whereas Global Moran’s I and APAM univariate analysis revealed subtle differences between methods. Spatial KPIs serve as important complementary metrics for performance evaluation in the design of robust traffic management systems.