A bank wishes to decide how many staff to schedule during its lunch period. During this period…

A bank wishes to decide how many staff to schedule during its
lunch period. During this period customers arrive at a rate
of 6 per hour and the enquiries that customers have (such as
opening new accounts, arranging loans, etc.) take on average 20
minutes to deal with. The bank manager feels that 3 staff
should be on duty during this period but wants to make sure that
the customers do not wait more than 3 minutes on average before
they are served.

The manager has been told by his small daughter that the
distributions that describe both arrival and processing times are
likely to be exponential. Therefore:

Calculate the utilization of the system where u = ra / (re x
m).

Using the formula for waiting time for a M/M/ m system,
calculate the average waiting time.

Interpret the results