Assessment of Single and Multi-Server Exponential Queuing Models in Banking System

Kolawole Daramola1, Ajeka Friday2, & Enoch Yabkwa Yanshak3
1Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
2Department of Computer Systems Technology, North Carolina A&T State University, USA
3Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
DOI – http://doi.org/10.37502/IJSMR.2025.8611

Abstract

Queuing occurs when the number of customers awaiting service exceeds the system’s service capacity, often leading to extended wait times and congestion. The banking sector in Nigeria is facing challenges related to prolonged queues, adversely impacting the nation’s economic growth. This article assessed both single and multi-server exponential queuing models. Performance indicators for both single and multi-server queuing models, such as utilization factor, average queue length, average system length, average queue waiting time, and average system waiting time, were computed and analysed. The result revealed that the (M/M/S): (FCFS/∞/∞) model outperforms the (M/M/1): (FCFS/∞/∞) model by minimizing customer waiting time from approximately 2.0 minutes to 0.03 seconds. The findings emphasized the efficiency of employing multiple servers; this shows that introducing more servers reduces the workload per server, potentially attracting more customers. Furthermore, a comprehensive analysis of cost implications and utilization factors served as a target for achieving a balance between minimizing cost and ensuring an optimal server level at the customer service of Access Bank Plc. The results indicated that for an optimal balance between service level and total cost, adopting the (M/M/4): (FCFS/∞/∞) model is recommended, as it results in a lower cost on the maintenance and servicing of queuing facilities (N9,104.99) compared to (N10,793.43).

Keywords: Queue, Arrival rate, Service rate, Single-Server, Multi-server model

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