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IEOR 161 Operations Research II
University of California, Berkeley
Spring 2008
Homework 11 Solution
Chapter 6.
13. Let the number of customers in the shop be the state. We then have a birth and
death process with
λ
0
=
λ
1
= 3
μ
1
=
μ
2
= 4
Therefore
P
1
=
3
4
P
0
P
2
=
3
4
P
1
= (
3
4
)
2
P
0
Solve
∑
2
i
=0
P
i
= 1 to get
P
0
=
16
37
.
(a)
P
1
+ 2
P
2
= 30
/
37.
(b)
P
0
+
P
1
= 28
/
37
(c) Now
μ
= 8, and solve the problem again to get
P
0
0
= 64
/
97. The proportion of
customers who enter the shop is
P
0
0
+
P
0
1
= 88
/
97.
The business he does would improve by
λ
(88
/
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Unformatted text preview: 97)Î» (28 / 37) = 0 . 45 customers per hour. 17. Let the state be 0 if the machine is up, i when it is down due to a type i failure, i = 1 , 2. The balance equations are Î»P = Î¼ 1 P 1 + Î¼ 2 P 2 Î¼ 1 P 1 = Î»pP Î¼ 2 P 2 = Î» (1p ) P P + P 1 + P 2 = 1 Solve them to get P = (1 + Î»p Î¼ 1 + Î» (1p ) Î¼ 2 )1 P 1 = Î»pP Î¼ 1 P 2 = Î» (1p ) P Î¼ 2 1...
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This note was uploaded on 03/03/2009 for the course IEOR 161 taught by Professor Lim during the Fall '08 term at University of California, Berkeley.
 Fall '08
 Lim
 Operations Research

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