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 El Con Mall for the week. Previous experience indicates that , on the average, 9 persons per hour request a test. Assume arrivals are Poisson distributed from an infinate population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with FCFS discipline. A) What average number in line can be expected? B)What averagenumber of persons can be expecgted to be in the system? C) What is the average amount of time that aperson can expect to spend in line? D) On the average, how much time will it take to measure a person's blood pressure, including waiting time? E) On weekends, the arrival rate can be expected to increase to over 12 per hour. What effect will this have on the number in the waiting linbe?

Explanation / Answer

arrival rate =9 ,

service rate =60/5=12

a)Lq=2/(-) =92/12(12-9)=2.252 persons can be expected

b)Ls =/(-) =9/(12-9) =3 persons

C)Wq =Lq/ =2.25/9 =0.25 hour or 15 minutes

d)Ws=Ls/ =3/9 =(1/3)hour or 20 minutes

e)

for 9 persons/hour ----->2.25 persons are expected

12 person/hour----->

=12*2.25/9 =3 persons

so the number on the waiting line would increase by 1.

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