My Math Forum Markov chains

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 September 19th, 2016, 05:56 AM #1 Newbie   Joined: Sep 2016 From: Sydney Posts: 2 Thanks: 0 Markov chains Hi, can someone help me with part (c) of this question? Thank you very much. Below is the full question. In this problem, we model a queue using a Markov chain. (the queue might represent, for example, customers waiting to buy something at a shop, a web server attempting to respond to page requests, or students waiting during office hours.) Suppose that a certain queue may contain 0, 1, or 2 items. It is not possible for it to contain 3 or more items. At each time step, one of two things can happen: (i)with probability 1/3, one item is removed from the queue, if there is an item to remove (and otherwise nothing happens), or (ii) with probability 2/3, one item is added to the queue, if there is enough space (i.e. if there are not already 2 items in the queue) (and otherwise nothing happens). (a) Formulate a finite Markov chain that describes this system. (b)If the queue starts off empty, after 4 time steps what is the probability that it is again empty? (c) In the long term, what is the average rate at which items are removed from the queue?
 September 19th, 2016, 08:47 AM #2 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions What have you got so far?
 September 19th, 2016, 05:30 PM #3 Newbie   Joined: Sep 2016 From: Sydney Posts: 2 Thanks: 0 I think that I have to calculate the steady state vector for c and I have done so but I am not sure how to continue from there.

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