An Investigation of Multi-server Queuing Analysis to Assess Hospital Healthcare Systems' Operational Effectiveness

Mohammed Idris Umar *

Department of Statistics, Nasarawa State University, Keffi, Nigeria.

M. U. Adehi

Department of Statistics, Nasarawa State University, Keffi, Nigeria.

Abubakar, Muhammad Auwal

Department of Statistics, Nasarawa State University, Keffi, Nigeria.

*Author to whom correspondence should be addressed.


Prolonged wait (queue) times in medical outpatient departments are a growing concern in Nigerian hospitals/clinics, due to a variety of consequences such as overcrowding, patients leaving in anger without being attended to, and being stressed for not staying too long in the system. The primary goal of this paper is to research various techniques or methods for reducing long queues. Patients who wait for minutes, hours, days, or months to receive medical services may incur waiting costs. The time spent in the queue could have been better used elsewhere. This paper aims to determine an optimal server level while keeping total system costs to a minimum, including expected service costs and waiting costs in a multi-server system, to reduce patient congestion in the hospital. Data for the study was collected in two ways. The secondary method was first used to identify the most congested OPD among the numerous OPDs considered in the study. The performance measures costs were then calculated using primary data. The performance measures of the queuing system were calculated using TORA optimization software. MS Excel was used to calculate the costs and plot the charts. Based on the results of the analysis, it was suggested that one physician be added to the hospital's medical OPD to reduce patient overcrowding and wait times. As a result, this call for refocusing is issued to improve overall patient care in our cultural context while also meeting the needs of patients in our society.

Keywords: Multi-server, utilization factor, reneging, waiting costs, service costs, and servers

How to Cite

Umar, M. I., Adehi, M. U., & Auwal, A. M. (2024). An Investigation of Multi-server Queuing Analysis to Assess Hospital Healthcare Systems’ Operational Effectiveness. Asian Journal of Probability and Statistics, 26(3), 80–89.


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