Reneging behaviour estimation based on incomplete observational data of the server

Effective management of queuing systems is critical for maximizing operational efficiency and customer satisfaction across various service industries, from banking to call centres. This study presents an approach to estimating reneging times in methods characterized by incomplete observational data of servers. Reneging, where customers abandon the queue before receiving service, poses a considerable challenge due to the lack of direct observation of customer departure times. We developed a discrete-event simulation model within a Python-based M/G/1 queuing framework to investigate both state independent and state dependent reneging behaviours, where reneging times are exponentially distributed. Utilizing partial data available from the server's perspective, such as the initial queue position and discovery times of the reneged customers, when they are called but absent. We propose and evaluate three distinct estimation methods for predicting the interval before customers abandon the service queue. Our findings demonstrate the effectiveness of these methods under various system configurations, displaying dynamics between service time distributions, reneging behaviours, and queuing parameters. This study enhances queuing theory by introducing practical methods that help service providers better understand and manage queues, even with limited data.