At a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average hair cut taking 19 minutes. It is assumed that because of excellent reputation, customers were always willing to wait. Calculate the following a. Average number of customers in the shop and average numbers waiting for a haircut b .Percentage of time arrival can walk in right without having to wait c. The percentage of customers who have to wait before getting into the barber’s chair

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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At a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average hair cut taking 19 minutes. It is assumed that because of excellent reputation, customers were always willing to wait. Calculate the following

a. Average number of customers in the shop and average numbers waiting for a haircut

b .Percentage of time arrival can walk in right without having to wait

c. The percentage of customers who have to wait before getting into the barber’s chair

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