Study of Queuing Theory M/M/M and Optimization Services Teller at Retail Banking

The research was conducted at retail banking in order to determine significant differences the average number of customers and the average waiting time in the system and the queue of Split Decision System. As well as the significance and probability of no customers in the system utilization teller services from Split Decision Systems at retail banking. The elected locations for sample were Bank Mandiri Ahmad Yani Branch and Bank Central Asia Sudirman Branch in Pekanbaru. Data was collected with a probability sampling technique by random sampling, so the data were taken at random in the queuing system is running at 10:00 to 12:00 and 13:00 to 15:00 hours on weekdays based on observations. Observation is by observing and measuring the amount of the average customer arrival (x) and the average number of customers served (μ) in a period of time (hours) in the queuing system. The results of the test sample t test showed that there were significant differences in the average number of customers and the utility both in the system and in the queue of Split Decision System. This is indicated the t value is smaller than the table t, and no significant difference on average waiting time and the probability of no customers in both the system and the queue of Split Decision System. This is indicated the t value greater t table is obtained, and for the number of teller enabled to obtain the optimal cost is 7 teller's for a transaction 25 million in the Mandiri Bank.