Blood Pressure

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To raise awareness of individuals own blood pressure, the Heart Association plans to install a free blood pressure testing booth in Tyler Mall for the week. Previous experience indicates that, on the average, 10 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 five minutes each. Determine
a) What average number in line can be expected?

L = λ2/µ (µ
λ)

Average number waiting in line= (arrival rate) 2/service rate (service rate arrival rate)

102/12(12-10)

4.17

About 4 individuals can be expected

b) What average number of persons can be expected in the system?

L = λ/µ

Blood Pressure

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λ Average number in system= arrival rate/(service rate arrival rate)

10/12-10

5 individuals can be expected

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

W = L/ λ

Average time waiting in line = average number waiting in line/arrival rate

4.17/10

0.417 hour

~25 minutes (25.02)

d) On the average, how much time will it take to measure a person’s blood pressure, including waiting time?

W = L/λ

Blood Pressure

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Average total time in the system = Average number in system/arrival rate

5/10

0.5 hours

30 minutes

e) On weekends, the arrival rate can be expected to over 12 per hour. What effect will this have on the number in the waiting line?

At 10 per hour:

L = 102/12(12-10) = 4.17

Using ratio and proportion:

(10/4.17)(12/x)

5 individuals

Blood Pressure

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Additionally, on weekends, the arrival rate can be expected to increase to nearly 12 per hour.

f) Explain the effect this will have on the number in the waiting line.

An increase in the number of people intending to measure blood test will lead to more time being spend in the system

g) List ten considerations you would take into account before installing the machine.

1.   The average amount of time it takes to measure
2.   The average number of individuals in the system
3.   Average amount of time an individual is expected to spend in the system
4.   The population
5.   Location
6.   Average number of persons on a daily basis
7.   Arrival rate
8.   Days of the week that have the largest number of arrivals
9.   Service rate
10.   The effect of the arrival rate on the individuals on the queue