Question

Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns three tellers. The service times of the customers are i.i.d. exponential random variables with mean 4 minutes. Compute the expected amount of time in which three tellers are assigned to customer service during an 8-hour day, assuming the lobby is empty at the beginning of the day.

Answer 1