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 7 persons per hour request test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of six minutes each. Assume the queue length can be infinite with FCFS discipline.

a. What average number in line can be expected? Round answer to 2 decimal places.

Average number expected _____ people

b. What average number of persons can be expected to be in the system? Round answer to 4 decimal places.

Average number of persons _____ persons

c. What is the average amount of time that a person can expect to spend in line? Round 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 answer to 4 decimal places.

Time taken _____ hours

Answer 1

Following are the relevant data :

Arrival rate = a = 7 per hour

Service rate ( 6 minutes each ) = s = 10 /hour

a) Average number in line = a^2/ S x ( S – a ) = 7 x 7 / 10 x ( 10 – 7 ) = 49 /30 = 1.63

b) Average number of persons in the system = a / S -a = 7/ ( 10 – 7 ) = 7/3 = 2.3333

c) Average amount of time a person will spend in line = a / S x ( S – a ) = 7 / 10 x ( 10 – 7) = 7/30 = 0.2333 hours

d ) Time it will take to measure blood pressure including waiting time = 1/ S -a = 1/ ( 10 – 7 ) = 1/3 = 0.3333 hours