An Empirical Study of Waiting Line Optimization in Guarantee Trust Bank (Gtbank) Using Queuing Models

This study examines the waiting line system of Guaranty Trust Bank (GTB) using empirical queueing analysis to evaluate service efficiency, customer waiting costs, and the suitability of classical queueing assumptions. Primary data were collected from ATM terminals and the banking hall at (GTBank) in Ogbomoso, Nigeria, with interarrival and service times recorded in minutes. The analysis employed descriptive statistics, Kolmogorov–Smirnov goodness-of-fit tests, and parameter estimation under Gamma and Lognormal distributions. Graphical diagnostics through histograms and QQ-plots revealed that both arrival and service-time distributions were right-skewed with heavy tails, deviating from exponential assumptions. The findings show that customer arrivals are clustered rather than random and that service durations vary widely due to differences in transaction complexity. Consequently, the M/M/1 model’s memoryless assumption was found inadequate, while M/G/1 or data-driven simulation frameworks provide more realistic representations. The study concludes by recommending operational adjustments such as load balancing among ATMs, staff reallocation, and customer education to reduce waiting times and optimize service delivery.