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316_F07_HW6

# 316_F07_HW6 - IOE 316 Fall 2007 Homework 6 Due MONDAY...

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IOE 316 Fall 2007 – Homework 6 Due MONDAY December 10, 2007 NOON (12pm) Note: To turn in your homework, you can either slide it under instructor’s office door (1783 IOE) by noon, or bring it to Arleigh’s office hours that morning. No late homework will be accepted. 1. (15 points) In the summer, an air conditioner is in one of three states: (0) off, (1) low, or (2) high. While off, transitions to low occur after an exponential time with expected time 3 minutes. While in the low state, transitions to off or high are equally likely and transitions out of the low state occur at rate 2 per minute. When the system is in the high state, it makes a transition to the low state with probability 2/3 or to the off state with probability 1/3. The time spent in the high state is an exponential random variable with a mean of 2 minutes. Model this air conditioning system using a continuous time Markov chain (CTMC). (a) (5 points) Draw the CTMC rate diagram, clearly label your states and transition rates ( q ij ’s) (b) (5 points) Find transition rates out of the states ( v i ’s) and transition probabilities ( P ij ’s).

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