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, 7.0 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 six 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

This can be modeled using the M/D/1 queuing system -

= Average arrival rate = 7 per hour
= Average service rate = 10 per hour

(a)

The average number in line that can be expected (Lq) = 2 / 2( - ) = 49 / (2*10*3) = 0.817

(b)

The average number in system that can be expected (Ls) = Lq + (/) = 0.817 + (7/10) = 1.517

(c)

The average amount of time that a person can expect to spend in line (Wq) = Lq / = 0.817/7 = 0.1167 hrs.

(d)

The average amount of time that a person can expect to spend in system (Ws) = Wq + (1/) = 0.1167+0.1 = 0.2167 hrs.

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