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11.08.Spring

# 11.08.Spring - ISyE 3232A/C Spring 2008 Homework 11 Due by...

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ISyE 3232A/C - Spring 2008 Homework 11 Due by 3PM, Thursday 4/17/2008 for Section A Due by 9AM, Friday 4/18/2008 for Section C Homework 11 1. Consider the continuous-time Markov chain with state space S = { 1 , 2 , 3 , 4 , 5 } and generator matrices given below. For each one, (i) derive the embedded Markov chain transition matrix; (ii) classify the states; and (iii) compute the steady-state probabilities for each irreducible set of recurrent states of the continuous-time Markov chains. (a) P = - 1 1 0 0 0 2 - 5 2 1 0 1 0 - 4 0 3 3 1 0 - 6 2 0 0 0 5 - 5 (b) P = - 1 1 0 0 0 2 - 4 2 0 0 1 0 - 4 0 3 0 0 0 - 2 2 0 0 0 5 - 5 (c) P = 0 0 0 0 0 2 - 4 2 0 0 1 0 - 4 0 3 0 0 0 - 2 2 0 0 0 0 0 2. Consider a shoeshine store consisting of two chairs—chair 1 and chair 2. A customer upon arrival goes initially to chair 1 where his shoes are cleaned and polish is applied. After this is done the customer moves on to chair 2 where the polish is buffed. The service times at the two

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