Answer:
Arrival rate
1 every 3 minutes
1 minute = 1/3 = 0.33
60 minutes = 0.33*60 = 19.8 = 20 per hour
λ = 20 per hour
Service Rate
1 every 2 minutes
1 minutes = 1/2 = 0.5
60 minutes = 0.5*60 = 30 per hour
µ = 30 per hour
a. Utilization of Teller Machine
P = λ / µ
P = 20/30
P = 66.67%
b. Average number of customers in line
Lq = pL = (λ/µ) (λ/µ- λ)
= (20 / 30) (20 / 30 - 20)
= 20/30 * 20 / 10
= 1.33 customers
c. Average number of customers in the system
L = (λ/µ- λ)
= 20 / 30 - 20
= 20 / 10
= 2 customers
d. Average time customer spends in line
Wq = λ/[µ*(µ- λ)]
= 20 / [30 * (30-20)]
= 20 / 30 * 10
= 0.06667 hours or 4 minutes
e. Average time customers spend in the system
W = 1/(µ- λ)
= 1 / 30 - 20
= 1/10
= 0.10 hours or 6 minutes
f. Probability that there are 3 customers in the system
Pn = (1-p)*p^n
= (1 - 20/30) * (20/30)^3
= 0.3333 * 0.296296
= 0.09876
g. Probability that there are two or more customers in the system
= 1 - P(0) - P(1)
= 1 - (1 - 20/30) * (20/30)^0 - (1 - 20/30) * (20/30)^1
= 1 - 1/3 - 2/9
= 4/9
= 0.4444
