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University of Minnesota Markov Chain and Equilibrium Probability Questions

University of Minnesota Markov Chain and Equilibrium Probability Questions

Question Description

I’m working on a probability question and need an explanation to help me study.

A storage facility has space for 3 containers. During each interval,

each of the k containers in storage, where k may be anything from 0 to 3,
is removed with probability p, independently of the other containers in
storage. Also, during each interval, exactly one container arrives with
a request to store it. It is accepted if there is space (after possible
departures described by the process with probability p), and is turned
away otherwise. Write down the transition matrix for the Markov chain
that best describes this. What is the equilibrium probability that the
incoming container will be turned away?

You can compute the last answer just for p = 1/7, but write down the
matrix for general p.

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