Dissertation (MSc Statistics)Statistics is one among the old and wide discipline spread across the global. As many studies and topics have been researched, published and presented in various setup and purpose. Some topics or areas of statistics are extensively covered in those researches in some areas. The study on queuing has not been done extensively in Tanzania. The queuing is a common practice to all public service centres where the demands surpass the supply. This study investigates the performance of queuing system at National Micro Finance Bank (NMB) Uluguru branch in Morogoro Tanzania. A daily observations data were recorded in a period of five days from Monday to Friday to find the distribution pattern of the arrival and the service time through fitting them in poison and exponential distribution respectively, to determine the average waiting time in a queue by using the M/M/C mathematical model, and to monitor waiting time in a system by using control chart. The results of the findings showed that the arrival time and service time follows poison and exponential distribution respectively. Also the results shows that the average waiting time is low as it has been indicated by average weekly service rate of the customers which is 0.62cust/min. Likewise, the findings showed the performance of the system is better as indicated by the theoretical control chart that the waiting time for all days except Wednesday are in control.