Stochastic

A what is the probability all three cabs are busy

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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 long-run 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.

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