MATHEMATICAL ANALYSIS OF NON – HOMOGENEOUS QUEUEING SYSTEM IN A BANKING HALL

Over the years, queues in banks have been a source of concern to most bank managers and their customers. This project work seeks to carry out a mathematical analysis of non-homogeneous queueing system in a banking hall and develop approximate queueing models that will make for optimal utilization of the tellers and consequently, improve service delivery to the bank’s customers. The study analyzed the arrival process, service process and queue discipline in Guaranty Trust Bank, Maitama branch, Abuja with the primary goal of establishing their interrelationship from the perspective of non-homogeneous processes. Furthermore, the study presented the application of chaotic queueing model to capture transient behavior in arrival rates using observed data. Four (4) different queues of single stage waiting lines with multiple servers were identified in the banking hall and primary data on the arrival and service processes were collected during 20 working days between 8.00am and 5.00pm by direct observation. The data was analyzed using an M / M / c queueing model and the results showed an average service rate of about 3.5 minutes and an average utilization rate that is less than 50%. Also, the average time customers spend on the queue was estimated to be less than 1 minute with the probability that the queue will be empty ranging from 0.04 to 0.43. These led to the conclusion that the service rate was acceptable. This implies an efficient service delivery in the banking hall with little or no queues, even though the system was busy all the time.