Abstract
The mathematical study of waiting lines is mainly concerned with queue performance measures where several applications have been drawn in past studies. Among the vast uses and applications of the theory of queuing system in banking halls, is the main focus of this study where the theory has been used to solve the problem of long queues as witnessed in banks leads to resource waste. The study aims to model the waiting times for queues in selected banks within Eldoret town, Kenya. The latter component was put under D/D/1 framework and therein its mean derived while the stochastic component was put under the M/M/c framework. Harmonization of the moments of the deterministic and the stochastic components was done to come up with the mean of the overall bank queue traffic delay. The simulation was performed using MATLAB for traffic intensities ranging from 0.1 to 1.9. The results reveal that both deterministic and the stochastic delay components are compatible in modelling waiting time. The models also are applicable to real-time bank queue data whereupon simulation, both models depict fairly equal waiting times for server utilisation factors below 1 and an infinitely increasing delay at rho greater than 1. In conclusion, the models that estimate waiting time were developed and applied on real bank queue data. The models need to be implemented by the banks in their systems so that customers are in a position to know the expected waiting time to be served as soon as they get the ticket from the ticket dispenser.