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Question

7. A small barbershop, operated by a single barber, has room for at most two customers.

Potential customers

arrive at a Poisson rate of three per hour, and the successive service

times are independent exponential random variables with mean 1 hour. What is the average 4

number of customers in the shop? 


My answer in the image below. Please verify my answer. Thanks!


sol7.jpg

sol7.jpg

W
7. arrival ~ Poi( 3 / hour )
4
Service ~ exp ( 4 / hour )
Find Stationany distribution
G = =3 3 0
4 -7 3
10 4 - 4.
[ To I T/2 3 3 0 - 0
4
9 3
4- 4
-31+ 41 =0
3 To - 7 71 + 4 1 1250
3 71 - 4 712=0
37+ 2 ( 37 )
= 12+18
3 1To= 4 7 1 1
37
371=4 The
30
37
To ( 1+ 4 + 76 ) = 1
16
37

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