Answer:
A) probability that an arriving customer will wait in line is 67%
B)the probability that both windows are idle is 0.33
C) the average length of the waiting line is 1.33
D)it would not be possible to offer a reasonable service with only one window
Step-by-step explanation:
arrival rate: δ = 20 x 0.80 = 16 customers per hour
service rate: μ = 2 × (60/5) = 24 customers/hour
Utilization factor is given as;
Φ = δ/μ
So, Φ = 16/24 ≈ 0.67
A) the probability that an arriving customer will wait in line is;
16/24 x 100% ≈ 67%
B) probability that both windows are idle is;
P(x=0) = 1 - 0.67 = 0.33
C) The average number of customers in the post office will be;
L_s = Φ/(1 - Φ)
L_s = 0.67/(1 - 0.67)
L_s = 0.67/0.33
L_s ≈ 2 customers
Thus, the average length of the waiting line is;
L_w = L_s - Φ
L_w = 2 - 0.67
L_w = 1.33
D) this part demands that we find the utilization factor with only one window.
Thus;
arrival rate: δ = 20 x 0.80 = 16 customers per hour
And
service rate: μ = 1 × (60/5) = 12 customers/hour
Thus, Utilization factor = 16/12 = 1.33
Thus, it would not be possible to offer a reasonable service with only one window
