In queuing theory one deals with the mathematical analysis of the performance of queuing systems. In our daily lives customers encounter queues while seeking services in institutions. The increase in the number of customers has resulted to congestion at revenue collection points in Kenyan towns. There is therefore need to study the queuing systems to identify possible remedies. This study sought to fit a queuing model to bus park revenue collection point as a preliminary action in studying the congestion problem in Kisii town, Kenya. The study considered and collected data on the inter-arrival times, service times and the number of servers at Kisii Bus Park Revenue Collection Point. The inter-arrival and service times were plotted and compared to a plot of a theoretical exponential distribution. The inter-arrival times resembled a theoretical exponential distribution with a parameter 1.022 and the service times resembled a theoretical exponential distribution with a parameter 1.209. Further, Kolmogorov Smirnov and Anderson Darling goodness of fit tests were conducted to determine if the inter-arrival and service times were exponentially distributed. In both cases, the test statistics were less than the critical value. The study therefore established that the inter-arrival and the service times could be modeled as exponential hence Markovian. The revenue collection point used two servers. This study assumed that the servers followed the same service distribution. This study concluded that the inter-arrival and the service times had an exponential distribution and the queuing model used was M/M/2.