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 Con Mall for the week. Previous experience indicates that on average 140 persons per hour request a est. Assume ar vals are Posson distributed rom an infinite population Bood pressure measurements can be made a constan me d three 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 people b. What average number of persons can be expected to be in the system? (Round your answer to 3 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 takenhouns

Explanation / Answer

a. What average nuumber in line can be expected?

Solution:

Lq = 2/µ(µ- )

µ=60/3 (1 hour i.e. 60 minutes divided by 3 minutes guven in problem)

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

= 142/20(20-14)

= 1.633

= 2 customers .............Answer

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

Solution:

Ls = /µ-

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

=14/(20-14)

= 2.333

= 2 customers...............Answer

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

Solution:

Wq = Lq/

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

= 1.63/14

=0.11 hours..............Answer

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

Solution:

Ws = Ls/

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

= 3/14

=.21 hrs.............Answer

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