To support National Heart Week, the Heart Association plans to install a free bl

Question

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, 3 persons per hour request a test. Assume arrivals are Poisson from an infinite population. Blood pressure measurements can be made at a constant time of four minutes each. Assume the queue length can be infinite with FCFS discipline. a. What average number in line can be expected? (Round your answer to 4 decimal places.) Average number expected people b. What average number of persons can be expected to be in the system? (Round your answer to 4 decimal places.) Average number of persons c. What is the average amount of time that a person can expect to spend in line? (Round your answer to 4 decimal places.) Average amount of time hours d. On the average, how much time will it take to measure a person's blood pressure, including waiting time? (Round your answer to 4 decimal places.) Time taken hours

Explanation / Answer

This ia M/M/1 queueing model .

a. Arrival Rate, = 3 per hour, Service rate, = 60/4 = 15 per hour

Average number of expected people in line = = 2/(-) = 3^2/15/(15-3) = 0.0500 people

b. Average number of persons expected to be in the system = /(-) = 3/(15-3) = 0.2500 people

c. Average amount of time that a person can expect to spend in line = /(-) = 3 / 15 / (15-3) = 0.0167 hours

d. Average time it takes to measure a person's blood pressure, including waiting time = 1/(-) = 1/(15-3) = 0.0833 hours

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