Abstract:
Queuing model is very essential in statistical modelling to the continuous growth of organizations and businesses. They give clear procedures to be followed by the organization in order to get the targeted output. This is mostly the case in production companies, financial institutions and some businesses. The queuing model helps them develop a mechanism of optimizing their output, fast and efficient services to their customers. Supermarkets will always wish to avoid losing customers to their competitors due long queues and slow service delivery. Most of the supermarket have with time increased the number of its service points in a step to counter the endeavor growing population which leads to an increased number of customers on the premises. This brings in the need for a numerical queuing model for the supermarkets. This helps the supermarket develop and properly planned service delivery strategy. In this research, the main aim is showing that queuing theory satisfies the model when tested with the real-case scenario. The data used in this research was obtained from NSNB archives as well as through observation. The data was analyzed basing on the queuing theory. Little’s theorem becomes very essential in deriving certain quantities using a multi-server queuing model with four servers (M/M/4 queuing model). The quantities analyzed includes: arrival rate (the frequency at which the customers are joining the arriving), service rate (the number of customers served per unit time), average utilization of the system (the expected fraction of time the servers are busy), average number of customers in the system, average number of customers in the queue, the average time a customer spends in the system, the average time a customer spends waiting in the queue before being served and the probability of having n customers in the system at some time t. All this quantities are calculated and compared to the observed values so as to come up with a suitable solution to the growing queue length in the supermarket. This research was concluded by discussing the importance of the queuing model analysis to a busy supermarket premises.
