Asian Journal of Mathematics and Computer Research

Peak-hour congestion remains a recurrent operational problem in retail banking, particularly when customer arrivals exceed available teller capacity. This study applies an M/M/c queueing model to evaluate teller staffing requirements in a retail banking system during high-demand service periods. Customer arrivals were modelled as a Poisson process, service times were assumed to be exponentially distributed, and the system was assessed under a first-come, first-served discipline with multiple parallel tellers. Field observations over 10 working days produced an average arrival rate of 30 customers per hour and an average service rate of 8 customers per hour per teller. Using these parameters, traffic intensity, probability of waiting, expected queue length and average waiting time were computed for four to seven active tellers. The results show that four tellers produce high utilisation and substantial delay, with an average waiting time of approximately 26 minutes. Increasing teller capacity consistently reduces congestion; for seven tellers, recalculation gives a probability of waiting of about 0.103, an expected queue length of about 0.119 customers and an average waiting time of about 0.237 minutes. Sensitivity analysis indicates that increases in arrival rates or reductions in service rates rapidly worsen queue performance, especially as utilisation approaches full capacity. The study therefore shows that the M/M/c model can provide a practical quantitative basis for teller-staffing decisions during peak banking periods.