# sol7 - EE292 Analysis & Control of Markov Chains Prof. Ben...

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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.

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sol7 - EE292 Analysis & Control of Markov Chains Prof. Ben...

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