Question

To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in Walnut Square for the week. Past experience shows that an average of 10 people per hour request tests and the time to take the test is fixed at 5 minutes.

2A.What percentage of time would the booth be idle?

2B.How much time, on average, does the patron spend waiting in line?

2C.How long is the (waiting) line on average?

2D.If the booth is open 10 hours a day for seven days, what is the expected number of blood tests performed?

2E.How much total time will the patron have to spend to get their blood pressure checked (waiting in line and having the test performed)?

USING EXCEL

Answer 1

Arrival rate lambda = 10

Service rate mu =60/5 =12

Utilisation rho =lambda /mu = 10/12 =0.8333

Fraction idle time = 1-rho =1-0.8333 =0.1666 =16.66% of time

(ii) Waiting time in line Wq= rho /mu-lambda = 4.16/10 =0.416 hour

(iii) Length of line Lq = Wq * lambda =4.16

(iv) Number of tests = arrival rate* number of hours = 10*10*7 =700

(v) Time spent in system = Wq + 1/mu = 0.416+1/12 =0.4993 hours

Lambda	mu	rho	Wq	Lq	W	Hours per week	Weekly capacity	P(0)
10	12	0.833333	0.416667	4.166667	0.5	70	700	0.166667