Abstract

This paper deals with the Queueing theory and the analysis of queueing system by using probability curves. Starting with the basis of the distributions and important concepts of queueing theory, probability curves of Gamma distribution are used to analyse the banking service.

II. CONCLUSION

This paper studies the Queueing theory and by the use of probability curves the analysis of the queueing system. From the work surveyed above we have found arrival and service rates at the bank are different in different weeks. The conclusions are developed from the application of Gamma probability distribution. The arrival rate is higher in week 1. However, the higher arrival rate is offset by higher service productivity. Therefore, the probability of completing the service in 5 minutes in week 1 is 0.060361. The efficiency factor is not constant. The service productivity diminishes and as a result the probability in the second week drops to 0.054344. In the third week the rate of arrival decreases. Consequently, maintaining the same service rate as in the second week, the probability goes up to 0.074055. The service rate is less in the last week of the month as the arrival rates decrease considerably, the probability of completing the service with in less time peaks as compared to the remaining weeks.i.e0.087442.