Customers arrive at Rich Dunn\'s Styling Shop at a rate of 3 per hour, distribut

Question

Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Service times follow an exponential distribution, and Rich can perform an average of 6 haircuts per hour.

a) Find the average number of customers waiting for haircuts.____ customers ( round your response to two decimal places)

b) Find the average number of customers in the shop. ____ customers ( round your response to two decimal places)

c) Find the average time a customer waits until it is his or her turn. ____ customers ( round your response to two decimal places)

d) Find the average time a customer spends in the shop. ____ customers ( round your response to two decimal places)

e) Find the percentage of time that Rich is busy ____ customers ( round your response to two decimal places)

Explanation / Answer

Arrival rate = 3 per hour

Service rate µ = 6 per hour

a) Find the average number of customers waiting for haircuts.____ customers

= / (µ - ) = 3 / (6-3) = 3/3 = 1 customer

b) Find the average number of customers in the shop. 1.5____ customers

c) Find the average time a customer waits until it is his or her turn. ____ customers

Wq = W – 1/µ = 0.33 – 1/6 = 0.163 hours = 10 mins

d) Find the average time a customer spends in the shop. ____ customers

W = 1 / (µ -) = 1 /(6 -3) = 0.33 hours = 20 mins

e) Find the percentage of time that Rich is busy ____ customers

       = / µ = 3 /6 = 0.5 = 50 % time

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