# When a toner cartridge is empty it is sent to a

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Unformatted text preview: ulate a Markov chain model for the this system with state space {0, 1, 2, 12} where the numbers indicate the machines that are broken at the time. (b) Suppose that 1 = 1, µ1 = 2, 2 = 3, µ2 = 4. Find the stationary distribution. 151 4.8. EXERCISES 4.5. Two people are working in a small o ce selling shares in a mutual fund. Each is either on the phone or not. Suppose that salesman i is on the phone for an exponential amount of time with rate µi and then o↵ the phone for an exponential amount of time with rate i . (a) Formulate a Markov chain model for this system with state space {0, 1, 2, 12} where the state indicates who is on the phone. (b) Find the stationary distribution. 4.6. (a) Consider the special case of the previous problem in which 1 = 2 = 1, and µ1 = µ2 = 3, and ﬁnd the stationary probabilities. (b) Suppose they upgrade their telephone system so that a call to one line that is busy is forwarded to the other phone and lost if that phone is busy. Find the new stationary probabilities....
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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