A small branch bank has two tellers, one for receipts and one for withdrawals. Customers arrive to each teller's cage according to a Poisson distribution with a mean of 20/h. (The total mean arrival rate at the bank is 40/h.) The service time of each teller is exponential with a mean of 2 min. The bank manager is considering changing the setup to allow each teller to handle both withdrawals and deposits to avoid the situations that arise from time to time when the queue is sizable in front of one teller while the other is idle. However, since the tellers would have to handle both receipts and withdrawals, their efficiency would decrease to a mean service time of 2.4 min. Compare the present system with the proposed system with respect to the total expected number of people in the bank, the expected time a customer would have to spend in the bank, and the average idle time of the tellers.

2. Customer arrivals at a 7-Eleven is Poisson at the rate of 20 per hour. They can be assumed to spend an average of 12 minutes picking up merchandise, with the length of time having an exponential distribution. Two checkout counters provide service with a service rate of 15 per hour at each counter. We may also assume that the service times have an exponential distribution. Determine the limiting results for the following: (a) the distribution of the number of customers picking up merchandise and its mean; (b) the mean length of time the customers wait at the counter for service; (c) the mean total amount of time the customers spend in the store.

just tell the arrival rates and departure rates for Q.2.