Dissertation (MSc Statistics)This study studies the performance of queueing systems in the cafeterias at the University of Dodoma, Dodoma Tanzania. Data were recorded in a period of seven days from Monday to Sunday for all queues that is breakfast, lunch queue1 and 2 and dinner queue 1 and 2 at Rice phase 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/1 mathematical model, and to analyze the waiting time in a system by using statistical quality control chart. The results of the findings showed that the arrival time and service time for all queues in all sessions follows poison and exponential distribution respectively. Also the findings showed that the expected waiting time is high during breakfast as it has been indicated by the weekly service rate which is 0.479cust/min. Meanwhile during lunch and dinner the expected waiting time is low compared to breakfast. That is for lunch the service rate is 0.786cust/min and 0.792cust/min for queue 1and queue 2. While for dinner session the service rate is 0.740cust/min and 0.733cust/min for queue 1and queue 2. Similarly the findings showed the performance of the system is not good as indicated by the theoretical control chart that the waiting time for all queues are out of control