Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour. a) The average number of customers waiting for haircuts = ? enter your response here customers (round your response to two decimal places). b) The average number of customers in the shop = ? customers (round your response to two decimal places). c) The average time a customer waits until it is his or her turn = ? enter your response here minutes (round your response to two decimal places)

Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour. a) The average number of customers waiting for haircuts = ? enter your response here customers (round your response to two decimal places). b) The average number of customers in the shop = ? customers (round your response to two decimal places). c) The average time a customer waits until it is his or her turn = ? enter your response here minutes (round your response to two decimal places)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour.

a) The average number of customers waiting for haircuts = ?

enter your response here

customers (round your response to two decimal places).

b) The average number of customers in the shop = ?
customers (round your response to two decimal places).

c) The average time a customer waits until it is his or her turn = ?

enter your response here

minutes (round your response to two decimal places).

Expert Solution

Step 1 Introduction:

Here, given the data stated below,

The arrival rate is 2 per hour and the service rate is 6 per hour,

I would determine the answers for each question using the formulas, the detailed calculations are shown below,

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d) The average time a customer spends in the shop = ?

enter your response here

minutes (round your response to two decimal places).

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