Problem: Queuing

A bank has two tellers to service customers who want to conduct their banking business in person. The first teller is dedicated exclusively to personal banking customers who want access to their (non-commercial) bank accounts. The second teller is dedicated exclusively to commercial banking customers who want access to their business bank accounts. The bank maintains separate waiting lines for the different types of customers, and strictly adheres to a policy that personal banking customers will only be served by the first teller, and commercial banking customers will only be served by the second teller.

Customers of each type arrive randomly throughout the business day. On average, 30 personal banking customers and 10 commercial banking customers arrive at the bank per hour, and the time between arrivals for both types of customers is exponentially distributed. Teller 1 is capable of processing 40 personal banking customers per hour, while the more complex transactions required by business customers limit Teller 2 to servicing only15 customers per hour on average. Service times for both tellers have been observed to follow an exponential distribution.

a. How long on average is a personal banking customer in the bank? On average how many personal banking customers are waiting for service at any given time?

Average Time in the Bank (minutes) _________

Average Number Waiting (customers) _________ 

b. How long on average is a commercial banking customer in the bank? On average how many commercial banking customers are waiting for service at any given time?

Average Time in the Bank (minutes) _________

Average Number Waiting (customers) __________

c. The bank decides to cross-train the two tellers so that they are each capable of processing both personal and commercial banking customers. Customers now enter a single queue and are served by the first available teller. All of the information given about customer arrivals and service times remains unchanged.

Under the new configuration, how long on average is a banking customer in the bank? On average how many banking customers are waiting for service at any given time?

Average Time in the Bank (minutes) _________

Average Number Waiting (customers) _________