Answer:
Below is the solution to the given problem
Explanation:
a. What is the average number of customers waiting?
With one barber and exponential service, this system fits Model 1 in the text. λ = 3.000 per hour (given), μ= 60/17 = 3.529 per hour.
You are looking for Lq here.
Lq = λ[tex]^{2}[/tex] / μ(μ – λ) = [tex]3.00^{2}[/tex]/3.529 (3.529 – 3.000) = = 4.82 customers
b. What is the average time a customer waits?
Wq = Lq/λ = 4.82/3.00 = 1.607 hours = 96.40 minutes
c. What is the average time a customer is in the shop?
You are looking for Ws here, and need to calculate Ls first.
Ls = λ / μ(μ – λ) = 3.00/3.529 – 3.000= 5.671
Ws = Ls/λ = 5.671/3.00 = 1.890 hours = 113.4 minutes
d. What is the average utilization of Benny's time?
ρ = λ/μ = 3.00/3.529 = 0.85 = 85.0%
The average number of customers that are waiting will be 5 customers.
The average number of customers waiting will be:
= 3.00² / 3.529(3.529 - 3.0)
= 4.82 customers
= 5 customers
The average time that a customer will wait will be:
= 4.82/3.00
= 1.62 minutes
The average time a customer is in the shop will be:
Ls = λ / μ(μ – λ)
= 3.00/3.529 – 3.000 = 5.671
Therefore, average time will be:
= 5.671/3.00 = 1.890 hours
= 113 minutes
The average utilization of Benny's time will be:
ρ = λ/μ
= 3.00/3.529
= 85.0%
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