Question

to support national heart week the heart association plans to install a free blood pressure testing booth at the soda city market.the association will have 5 separate setup to test blood pressure.they predict 50 people/hour will request a test with a cva =1 .it takes and on avarage , 5mitutes to complete the test with standard deviation of 3 minutes.on avarage ,how many people should the association except to see in line,waiting to have their blood tested?

Answer 1

Average arrival rate, r_a = 50 per hr.
So, average interarrival time, ta = 1/50 hrs. = 1.2 minutes

Average service time, t_e = 5 minutes
Std. Dev of service time, s_e = 3 minutes

c_a = 1
c_e = s_e / t_e = 3 / 5 = 0.60

Numbe rof servers, m = 5

Utilization, u = t_e / m.t_a = 5 / (5*1.2) = 5/6

Compute the average waiting time for a person (CT_q) using the following formula:

So, CT_q = ((1 + 0.6^2)/2)*(5/6)^(SQRT(2*(5+1)) - 1)*5 / (5*(1 - 5/6)) = 2.603 minutes

So,

Average number of people waiting, L_q = CT_q / t_a = 2.603/1.2 = 2.17 persons