<p>Real-world service systems, such as call centres, hospitals, and transportation networks, often experience time-varying arrivals due to fluctuating demand patterns throughout the day. Accurately modelling these systems requires incorporating realistic characteristics. A commonly used approach for modelling time-varying arrival processes is the non-homogeneous Poisson process (NHPP), which allows the arrival rate to vary over time. Unlike the traditional Poisson process with a constant intensity, NHPP captures fluctuations in arrival patterns by incorporating a time-dependent intensity function. Estimating this intensity function is crucial for accurately modelling the time-varying arrivals. In this study, we explore the maximum likelihood estimation (MLE) method to estimate the intensity function of an NHPP. We model call arrivals using a simulated dataset from a customer care call centre and compare the actual and estimated intensity functions. The results demonstrate that the estimated intensity function provides a good fit to the data. Additionally, we model real-time bus arrival events using NHPP and estimate their intensity function. Python is the chosen programming language for this study.</p>