Consider the model of Conceptual Problem 4.2. Suppose the arrival rate is 20 cus
ID: 462442 • Letter: C
Question
Consider the model of Conceptual Problem 4.2. Suppose the arrival rate is 20 customers per hour and the average service time is 4 minutes. Compute the expected amount of time three tellers arc working during an 8-hour day, assuming there are no customers in the bank at the beginning of the day. Customers arrive at a bank according to a Poisson process with rate lambda per hour. The bank lobby has enough space for ten customers. When the lobby is full, an incoming customer goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is three or less, she assigns two tellers if the number is more than three but less than eight, and otherwise she assigns three tellers. The service times of the customers are iid Exp(mu) random variables. Let X(t) be the number of customers in the bank at time t. Model {X(t),t greaterthanorequalto 0} as a birth and death process, and derive the birth and death rates.Explanation / Answer
a=20 per hour{arrive}
b=60/2.5=24{capacity}
p={1-a/b}
0.16 no serving of jobs
a)utilization =84%