Missing in a network: gapfilling with kriging

Abstract

Kriging is a geostatistical technique widely used to predict values at unmeasured locations by leveraging spatial and temporal dependencies. Traditional kriging methods assume a continuous 2D space, where relationships between measurements are modeled based on Euclidean distance. However, this assumption is often inadequate for networked systems, where physical connectivity and network-specific distances provide a more realistic representation. To address this limitation, a variation of kriging has been developed for gap-filling time series data, particularly in hydrological networks such as river water levels. This project extends the application of kriging-based gap-filling methods to transportation networks, specifically to predict passenger loads along metro lines. Passenger load data is inherently spatio-temporal, characterized by station locations and scheduled service times. The study uses a modified kriging framework that incorporates Gaussian spatial and exponential temporal covariance models to account for the unique structure of the metro network. The methodology is applied to passenger data from the Frankston metro line, where predictions are evaluated against observed values using error metrics such as Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). Results demonstrate the potential of this approach in accurately modelling passenger loads, with implications for optimizing metro services and resource allocation. This study highlights the versatility of kriging methods in networked settings beyond traditional geostatistical applications, with potential relevance for other domains such as telecommunications and finance.