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 / μ(μ – λ) =
/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%