# solution

Tri-Cities Bank is planning to open drive-in teller service. Customers arrive randomly at the drive-in window, whose average inter-arrival time is 2 minutes. Assume the service provided at the drive-in window follows an exponential distribution. (Hint: use the excel template posted online for calculation)

Compute the following operating characteristics for each alternative of the four service alternatives are being considered below:
(a) Average number of cars waiting for service.
(b) Average time a car waits for service.
(c) Average time in the system.
(d) Average number of cars in the system.
(1) A single-channel operation where one employee serves customers. The average service time for this alternative is 1.5 minutes. (10 points)
(2) A single-channel operation where two employees work as a team to serve each customer. The average service time for this alternative (team) is 0.75 minutes. (10 points)
(3) A two-channel operation with two service windows and two employees. Newly arriving customers join one queue which feeds both service windows. One employee is stationed at each window serving customers arriving at the window. The average service time for each service window is 1.5 minutes. (10 points)
(4) There are two service windows and two employees. There is a separate queue for each of the service windows. Newly arriving customers randomly choose one of two queues. One employee is stationed at each window serving customers arriving at that window. The average service time for each service window is 1.5 minutes. (10 points)
(5) If the manager finds out the resulted waiting time in alternative
(1) is unacceptable. Among service alternative (2), (3) and (4), which option should the manager choose? And why?

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