Evaluating Single and Multi-Server Exponential Queuing Models: A Case Study of Access Bank PLC in Anyigba, Kogi State, Nigeria

Abstract

Queuing takes place when the number of individuals waiting in line surpasses the system's maximum capacity, occurring when the line extends beyond the available servers. The banking sector in Nigeria is facing challenges related to prolonged queues, adversely impacting the nation's economic growth. This issue results in customer dissatisfaction thereby hindering productivity and complicating patronage. Also, there is an economic loss to each person while remaining in the queue, which makes it essential to minimize, if not eliminate, the challenges of long queues in Nigerians banking system. This article assesses both single and multi-server exponential queuing models. Primary data was collected through direct observation and personal interviews, recording inter-arrival times and service durations from customer service unit of Access Bank Plc, Anyigba Kogi State. 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 analyzed. 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 minutes. This shows that introducing more servers reduces the workload per server, potentially attracting more customers. The analysis also indicates 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 of N 9,104.99 compared to N 10,793.43.

Keywords

• Queue
• Arrival Rate
• Service Rate
• Single-Server
• Multi-server Model