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 average, 14 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of four 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             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 taken              hours

Explanation / Answer

Arrival Rate=L=14/hr=14/60 per min= 0.233customers/min Sevice rate=m=1/4 customers/min=0.25 customers/min Probability of no unit in system(Po)=1-L/m=1-0.233/0.25=0.068 Average units in waiting line(Lq)=L^2/(m(m-L))=0.233^2/(0.25*(0.25-0.233))= 12.77388 Average units in system (K)=Lq+L/m=12.77+0.233/0.25= 13.702 Average time a units spends in waiting line(Wq)=Lq/m=12.77/0.233= 54.80687 mins Avg time a unit spends in system=Wq+1/m=54.8+1/0.25= 58.8 mins

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