Mathematical Modeling of Railway Reservation Systems: A Case Study with Differential Equations

Abstract

Railway reservation systems are complex networks that involve dynamic interactions between passengers, trains, and available seats. This paper presents a mathematical model of railway reservation systems using differential equations to capture the time-dependent behavior of seat occupancy, passenger demand, and reservation cancellations. The model is designed to optimize seat allocation, minimize overbooking, and improve overall system efficiency. A case study is conducted to validate the model, and numerical simulations are performed to analyze the system's behavior under various scenarios. The results demonstrate the effectiveness of the proposed approach in managing railway reservations and provide insights for improving real-world reservation systems.