American Research Journal of Biosciences

Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing theory which is the mathematical study of waiting lines or queue is suitable to be applied in the banking sector since it is associated with queue and waiting line where customers who cannot be served immediately have to queue(wait) for service. The aim of this paper is to determine the average time customers spend on queue and the actual time of service delivery, thereby examining the impact of time wasting and cost associated with it.We used the Markovian birth and death process to analyze the queuing model , which is the Multiple servers, single queue, (M/M/S) queuing model to analyze the data collected by observation from a bank and from the results obtained, the arrival rate is 0.1207 and the service rate is 0.156, the probability that the servers are idle is 0.44 which shows that the servers will be 44% idle and 56% busy, the expected number in the waiting line is 0.1361, the expected number in the system is 0.9098. The expected waiting time in the queue is 1.276 and the expected total time lost waiting in one day is 3.2664 hours, the average cost per day for waiting is ₦65.328 and from the calculation of the comparing solutions, the average cost per day from waiting is ₦7.966 which means that there had been a saving in the expected cost of ₦65.328 - ₦7.966 = ₦57.362. This means that with three servers, the average cost from waiting is reduced. Hence we concluded that the aim and objectives of this paper was achieved.