Abstract

This report presents an analysis of train delays within a railway network using Markov chain models. By simulating realistic delay data for ten trains over a specific route, we categorized delays into five distinct states and constructed both the transition count matrix and the transition probability matrix. These matrices quantify the likelihood of transitioning between different delay states, offering a probabilistic view of delay progression. The steady-state vector, derived from the transition matrix, indicates the long-term distribution of delay states, providing insights for long-term operational planning. These metrics are crucial for improving scheduling, maintenance, and resource allocation. The results demonstrate the robustness and interpretability of Markov chain models for predicting train delays, enabling railway operators to enhance service reliability and operational efficiency.