Question: A small branch office of a local bank has two tellers for which customers line up in a single queue. The customers are being served on an FCFS basis. It has been determined that the steady-state probability distribution for finding exactly n customers in the system, {Pn, n = 0, 1, 2, ...}, is P0 = (2/18), P1 = (5/18), P2 = (6/18), P3 = (3/18), P4 = (1/18), P5 = (1/18), and Pn = 0 for n = 6, 7, ....
a. Determine the expected number of customers in the system, L.
b. Determine the expected number of customers in the queue, Lq.
c. Determine the expected number of customers in the service facility.
d. Assuming that the mean arrival rate is six customers per hour, determine the expected time a customer spends in the system, W, and in the queue, Wq.
e. Determine the expected service time-the expected time a customer spends in the service facility-assuming that the two tellers are identical.