To raise awareness of individuals own blood pressure, the Heart Association plan

Question

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 the average number of persons in line will be,

(b) Explain Little’s theorem in layman’s terms, (c) Find the average number of persons in the system,

(d) Find the average amount of time a person can expect to spend in line,

(e) On average, how much time will it take to measure a person's blood pressure, including waiting time?

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.

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

Explanation / Answer

a. Arrival Rate, = 10/hour
    Service Rate, µ = 12/hour (Since 1 person takes 5 minutes)

Therefore, average number of persons in line
    = 2/µ(µ - )
    = 100/12(12-10)
    = 4.17

b. Little’s theorem states that:
The long-term average number of customers in a stable system L is equal to the long-term average effective arrival rate, , multiplied by the average time a customer spends in the system, W; i.e. L = W.

Suppose we want to find out the average number of customers in a store. Little's Law tells us that the average number of customers in the store L, is the effective arrival rate , times the average time that a customer spends in the store W. Assume customers arrive at the rate of 30 per hour and stay an average of 0.5 hour. This means that the average number of customers in the store at any time will be 15.

Average no. of customers (L) = 30*0.5 = 15

c. Average number of persons in the system
    = /µ(µ - )
    = 10/12(12-10)
    = 0.42

d. Average amount of time a person can expect to spend in line
    = /µ(µ - )
    = 10/12(12-10)
    = 0.42

Note: This question has 7 sub-parts. Only the first 4 sub-parts have been answered.

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