IV. (15%) Consider a two-server facility with a maximum capacity of 4 customers

Question

IV. (15%) Consider a two-server facility with a maximum capacity of 4 customers and a FCFS queue discipline. The following plot shows the number of customers in the system during the last 80 min. Using this information, answer the following questions (for the [0, 80]) time interval). Give a short justification of how you carry out the calculations and why E 4 3 0 0S 1015 20 25 30 35 40 4550 55 60 65 70 75 80 Time (in minutes) a. b. c. d. e. f. What is the average time in the system? What is the average arrival rate? For how long did the last customer stay in the system? What was her time in the queue? What is the average number of customers in the system? What is the average time in queue? What is the probability that there are at least one customer in queue?

Explanation / Answer

Lets chart the graph into the tabular form:

Idle Entry Wait Service Exit Client 1 2 2 0 4 6 Client 2 2 8 0 8 16 Client 3 0 12 0 6 18 Client 4 0 14 2 8 22 Client 5 2 20 0 18 38 Client 6 2 24 0 16 40 Client 7 0 36 2 14 50 Client 8 2 42 0 10 52 Client 9 0 48 2 12 60 Client 10 4 56 0 14 70 10 Total 24 6 110

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