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November 14th, 2009, 07:27 AM   #1
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Help about markov chains?

Each time unit a data multiplexer receives a packet with probability a, and/or
transmits a packet from its bu er with probability b. Assume that the multi-
plexer can hold at most N packets. This means that, if there are already N
packets in the queue, then no new packet can arrive. Let Xn be the number of
packets in the multiplexer at time n.
(a) Show that the system can be modeled by a Markov Chain.
(b) Find the transition probability matrix P.
(c) Find the stationary probability density function.

Can you help me with point (C). I don't understand the explanations in my textbook. And what do you think is it a 2 or 3 state markov chain.
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November 17th, 2009, 09:22 AM   #2
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Re: Help about markov chains?

It's an N+1 state chain, looking at the number of possible states for the multiplexer, no?

For a probability distribution to be stationary, it must be unchanged by the transition matrix P. So if u is the stationary probability distribution, we must have Pu = u. Use that to determine the relative probabilities for each state.
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