Asian Journal of Mathematics and Computer Research

Efficient queue management plays an important role in enhancing customer service delivery and operational efficiency at GCB Bank PLC, Tamale branch. Long customer waiting times arising from inadequate teller capacity can adversely affect customer satisfaction and the overall performance of banking operations. This study evaluated the performance of an \(M/M/c\) queueing model and determined the optimal teller capacity for improving customer service delivery at GCB Bank PLC, Tamale branch. Specifically, the study sought to determine the steady-state performance measures of the banking queueing system, examine the effect of increasing teller capacity through sensitivity analysis, and determine the optimal teller capacity that minimises customer waiting while maintaining efficient utilisation of banking resources. The study employed the classical \(M/M/c\) queueing model under the assumptions of Poisson customer arrivals, exponential service times, First-Come, First-Served (FCFS) service discipline, infinite calling population, unlimited queue capacity and steady-state operating conditions. An arrival rate of 45 customers per hour and a service rate of 12 customers per hour per teller were used in the analysis. The steady-state performance measures comprising traffic intensity, probability of waiting, expected queue length, average waiting time in the queue, average time spent in the system and expected number of customers in the system were computed for teller capacities ranging from eight to twelve. In addition, sensitivity analysis was conducted to evaluate the effect of increasing teller capacity on the performance of the banking queueing system. The results revealed that increasing teller capacity from eight to twelve progressively reduced traffic intensity from 0.46875 to 0.31250, the probability of waiting from 0.01473 to 0.00025, and the expected queue length from 0.01296 to 0.00011 customers. Similarly, the average waiting time in the queue decreased from 0.00029 hours to 0.0000024 hours, while the average time spent in the system reduced slightly from 0.08362 hours to 0.08334 hours. Sensitivity analysis further showed that increasing teller capacity substantially improved queue performance, although the magnitude of improvement decreased as more tellers were added. Additionally, the data showed that teller idle capacity increased continuously, indicating diminishing gains in service enhancement above a particular staffing level. Ten tellers were found to be the ideal staffing level for the banking system under the projected arrival and service rates based on the trade-off between queue performance and teller utilisation. According to the study’s findings, the \(M/M/c\) queueing model offers a useful framework for making decisions on how best to staff tellers and assess the performance of banking services. The results show that while maintaining the effective use of banking resources, optimal teller allocation can greatly minimise customer waiting times. The study recommends the adoption of queueing models in banking operations to support evidence-based staffing decisions and improve customer service delivery.