5. (14 points) To support National Heart Week, the Heart Association plans to in

Question

5. (14 points) To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on the average, 10 persons per hour request a test. Blood pressure measurements can be made following the Model 1 queuing (waiting line) model with an average service time of five minutes each.

a) What is the expected average number waiting in line for the testing booth?

b) What is the average amount of time that a person can expect to spend waiting in line?

c) On the average, how long will a person spend in the system (waiting for the testing booth and having the blood pressure test)?

d) What is the probability that a person arriving will have to wait for the testing booth?

Explanation / Answer

Arrival rate, = 10 persons per hour

Service rate, = 60 minutes per hour / average service time of 5 minutes = 60/5 = 12 per hour

a) Expected average number waiting in line, Lq = 2/(*(-)) = 102/(12*(12-10)) = 4.17

b) Average amount of time that a person can expect to spend waiting in line, Wq = Lq/ = 4.17/10 = 0.417 hour = 25 minutes

c) Average time in system, W = 1/(-) = 1/(12-10) = 0.5 hour = 30 minutes

d) Probability that a person arriving will have to wait for the testing booth = / = 10/12 = 0.833

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