Implementation of Queuing Model to Improve Operations in University Libraries

Stephen I. Okeke and Peter C. Nwokolo
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Stephen I. Okeke: Department of Industrial Mathematics and Health Statistics, International Institute for Machine Learning, Robotics and Artificial Intelligence David Umahi Federal University of Health Sciences, Uburu, Ebonyi State, Nigeria
Peter C. Nwokolo: Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

International Journal of Latest Technology in Engineering, Management & Applied Science, 2025, vol. 14, issue 5, 667-677

Abstract: The application of queuing models in university libraries is essential for enhancing service efficiency and improving overall user experience. These models help manage user flow, minimize waiting times, and optimize resource allocation by analyzing key factors such as arrival rates and service durations. Specifically, this study applied the M/M/1 queuing model, which assumes a single-server system with exponentially distributed inter-arrival and service times. The model was used to determine waiting times, queue lengths, and resource utilization in university library facilities. The analysis was conducted using QM (Quality Management) software for Windows. Deterministic numerical results were compared with software-made outputs to validate the model. Additionally, the study included graphical representations of probabilities and cumulative probabilities against the number of users in the system. Various plots were created to analyze utilization factors between the fixed parameters μ₠and μ₂ under varied arrival rates (λ). A regression equation was developed to examine the relationship between waiting time in the queue and utilization factors. Finally, the correlation between these factors was established to aid decision-making. By analyzing these parameters, library administrators can make informed decisions about staffing and service strategies to better meet user demand. In conclusion, implementing this mathematical queuing model significantly improves operational efficiency, user satisfaction, and the effective use of resources in university libraries.

Date: 2025
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