This week, you are visiting the FSA's regional branch in Valleyfield and during the three days you have been here,
you have noticed that customers waiting for services with the bank teller seem to be waiting a long time. The branch is open daily from 8 to 12 in the morning and 1 to 5 in the afternoon, with a one-hour lunch break. There is only one bank teller and it takes her an average of about 6 minutes to serve a client (the service time follows an exponential distribution). An average of 64 clients come to the bank each day and their arrival rate follows a Poisson distribution.
a) What are the arrival rate and service rate in the situation described above?
b) What is the average number of clients in the waiting line and the average time waiting in line?
c) What is the average total time spent in the system? Is this answer coherent with those given in a)? Justify.