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EE292
Spring 2006
June 7 , 2006
Prof. Ben Van Roy
Homework Assignment 7 : Solutions
1
We use the notation
s
for our state variable;
x
for queue length,
i
to indicate on/off.
S
=
{
(
x, i
) :
x
∈ {
0
,
1
, . . . ,
100
}
, i
∈ {
on, off
}}
. Further,
p
(
x,
on
)
,
(
x
+1
,
off
)
(
off
) = 0
.
75
for
x <
100
p
(
x,
on
)
,
(
x,
off
)
(
off
) = 0
.
25
for
x <
100
p
(
x,
on
)
,
(
x,
off
)
(
off
) = 1
for
x
= 100
p
(
x,
on
)
,
(
x,
on
)
(
on
) = 0
.
75
for
x
≤
100
p
(
x,
on
)
,
((
x

1)
+
,
on
)
(
on
) = 0
.
25
for
x
≤
100
p
(
x,
off
)
,
(
x,
on
)
(
on
) = 0
.
75
for
x
≤
100
p
(
x,
off
)
,
((
x

1)
+
,
on
)
(
on
) = 0
.
25
for
x
≤
100
p
(
x,
off
)
,
(
x
+1
,
off
)
(
off
) = 0
.
75
for
x <
100
p
(
x,
off
)
,
(
x,
off
)
(
off
) = 0
.
25
for
x <
100
p
(
x,
off
)
,
(
x,
off
)
(
off
) = 1
for
x
= 100
. The costs
g
(
s, u
)
are immediate from the question. Deﬁne
h
(
s, u
) = 1
if
x >
10
. We then have
the following linear program:
min
∑
s
∈S
∑
u
∈
U
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This note was uploaded on 02/15/2011 for the course EECS 6.231 taught by Professor Bertsekas during the Spring '10 term at MIT.
 Spring '10
 Bertsekas

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