Consider this situation: A manager is contemplating making changes to a single-server system that is expected to double the service rate, and still have just one server. For the sake of analysis, suppose the current system has an arrival rate of 8 customers per hour and a service rate of 10 customers per hour. If the service rate is doubled, find the impact that this would have on the average number of customers waiting in line. Compute the following ratio:

L_q2 / L_q1 = ? (Two decimal points)

L_q1 is the average number of customers waiting in line if the service rate doesnt change.

L_q2 is the average number of customers waiting in line if the service rate doubles.

8.

Many of a banks customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 90 seconds completing his or her transactions. Transaction time is exponentially distributed. Answer the following questions:

What is the average utilization of the teller machine in percentage (e.g. if it is 56% then write it as 56 without the percentage sign)?