# The average service time of the drive-in teller and the inside-bank teller?

A bank has one drive-in teller (who can serve customers without leaving their cars). The drive-in teller has a room (i.e., a queue) for one additional customer to wait. Customers arriving when the drive-in teller queue is full will park their cars and go inside the bank to transact business. Inside the bank, the waiting area is sufficient to accommodate all customers, and there is one teller who is as efficient as the drive-in teller in terms of serving the customers. The time enter image description herebetween- arrivals and service-time distributions are given below.

The problem is to estimate the system measures of performance in terms of the following: 1- The average service time of the drive-in teller and the inside-bank teller. 2- The average waiting time in the drive-in teller queue and the inside-bank teller queue. 3- The maximum inside-bank teller queue length. 4- The probability that a customer wait in the inside-bank teller queue. 5- The portion of idle time of the inside-bank teller. Moreover, the policy maker requires answers for the following questions: 6- Does the theoretical average service time of the service time distribution match with the experimental one? 7- Does the theoretical average inter-arrival time of the inter-arrival time distribution match with the experimental one? 8- If the drive-in teller queue can accommodate for two cars instead of one car, how does this affect the average waiting time in the drive-in teller queue and the inside-bank teller queue?

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