HW9 - IE 336 Apr 4 2011 Handout#10 Due Apr 15 2011 Homework...

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IE 336 Handout #10 Apr. 4, 2011 Due Apr. 15, 2011 Homework Set #9 1. Let p 12 ( t ) = 7 11 (1 - e - 11 t ) be the transition probability function from state 1 to state 2 in a continuous Markov random process. (Time t is measured in minutes.) (a) Find the steady-state probabilities. (b) Determine the transition diagram and the transition rate matrix. (c) At some point the process is in state 1. How likely is that 5 minutes later the process is still in state 1. (d) If the process spent last 15 minutes in state 2 how likely is that within the following 7 minutes a transition to state 1 will occur? 2. Let Λ = r + 2 0 0 3 q 0 0 - 7 - r 3 p 0 0 q 0 0 2 2 2 p - 8 t 2 t 2 1 2 s be the transition rate matrix of a continuous time Markov process. (a) Compute p , q , r , s , and t . Determine the transition diagram. (b) If the process is initially in state 5 determine the expected length of time before it reaches either state 1 or state 3.
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This note was uploaded on 01/19/2012 for the course IE 230 taught by Professor Xangi during the Spring '08 term at Purdue.

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HW9 - IE 336 Apr 4 2011 Handout#10 Due Apr 15 2011 Homework...

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