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 average, 13.0 persons per hour request a test Assume amvals are Poisson distributed 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 3 decimal places.) Average number expected 2817 people b. Whal average number of persons can be expected to be in the system (Round your answer to 3 decimal places.) Avcrage number of persons 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 wil it take to measure a person's blood pressure, including waiting time? (Round your answer to 4 decimal places.) Time taken hours

Answer 1

As given in the problem,

arrival rate, lamda = 13 persons per hour

service rate, mu = (60 minutes/ 4 minutes = 15) 15 persons per hour

a.

Average number in line can be expected

= lamda²/ mu (mu - lamda) = 13*13 / 15 (15 - 13) = 5.63 persons

b.

Average number of persons can be expected to be in the system

= lamda/ (mu - lamda) = 13/ (15 -13) = 6.5 persons

c.

Average amount of time that a person can expect to spend in line

= lamda/ mu *(mu - lamda) = 13/ 15 * (15-13) = 0.433 hours

d.

Average time to measure a person's blood pressure, including waiting time

= 1/ (mu - lamda) = 1/ (15-13) = 0.5 hours

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