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Unformatted text preview: server he moves on to the second server if it is free and leaves
the system if it is not. Suppose that server 1 serves at rate 4 while server 2
serves at rate 2. Formulate a Markov chain model for this system with state
space {0, 1, 2, 12} where the state indicates the servers who are busy. In the long
run (a) what proportion of customers enter the system? (b) What proportion
of the customers visit server 2?
Detailed balance
4.9. A hemoglobin molecule can carry one oxygen or one carbon monoxide
molecule. Suppose that the two types of gases arrive at rates 1 and 2 and
attach for an exponential amount of time with rates 3 and 4, respectively.
Formulate a Markov chain model with state space {+, 0, } where + denotes
an attached oxygen molecule, an attached carbon monoxide molecule, and 0 a
free hemoglobin molecule and ﬁnd the longrun fraction of time the hemoglobin
molecule is in each of its three states.
4.10. A machine is subject to failures of types i = 1, 2, 3 at rates i and a failure
of type i takes an exponential amount of time with rate µi...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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