- #1
caliboy
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1. Homework Statement [/b]
A barber shop has two chairs to cut hair and 10 people per hour enter the barbershop to get a haircut. . The average time it takes to get a haircut is 6 minutes. On this particular day, only one barber is cutting hair. Customers that enter the barber shop and use the other chair to wait in. Customers who see both chairs occupied, leave.
A) What is the system state probabilities?
B) What is the average number of customers that get a haircut in an hour
C) What is the average number of customers that get a haircut in an hour if both barbers are now working? There are no waiting chairs
2. Homework Equations
3. The Attempt at a Solution [/b]
A) I am really stumped by this one and would like some help. I believe this is a M/M/1/GD/c/∞ system; the formula I would use would be:
∏2=(1-ρ)/(1-ρc+1)
c=2
ρ=1
B) λ= 10
µ=10 people/hr ρ=10/10; =1
(10)*1=10 customers/hr
C) λ= 10
µ=20 people/hr ρ=10/20; =1/2
(20)*1/2=10 customers/hr
A barber shop has two chairs to cut hair and 10 people per hour enter the barbershop to get a haircut. . The average time it takes to get a haircut is 6 minutes. On this particular day, only one barber is cutting hair. Customers that enter the barber shop and use the other chair to wait in. Customers who see both chairs occupied, leave.
A) What is the system state probabilities?
B) What is the average number of customers that get a haircut in an hour
C) What is the average number of customers that get a haircut in an hour if both barbers are now working? There are no waiting chairs
2. Homework Equations
3. The Attempt at a Solution [/b]
A) I am really stumped by this one and would like some help. I believe this is a M/M/1/GD/c/∞ system; the formula I would use would be:
∏2=(1-ρ)/(1-ρc+1)
c=2
ρ=1
B) λ= 10
µ=10 people/hr ρ=10/10; =1
(10)*1=10 customers/hr
C) λ= 10
µ=20 people/hr ρ=10/20; =1/2
(20)*1/2=10 customers/hr