A total of N customers move about among r servers in the following manner. When a customer is served...

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A total of N customers move about among r servers in the following manner. When a customer is served by server i, he then goes over to server j , j ? i, with probability 1/(r ?1). If the server he goes to is free, then the customer enters service
otherwise he joins the queue. The service times are all independent, with the service times at server i being exponential with rate ?, i = 1, . . . , r. Let the state at any time be the vector (n 1 , . . . , n r ), where n i is the number of customers presently at server i, i = 1, . . . , (a) Argue that if X(t) is the state at time t , then {X(t), t 0}, is a continuous time Markov chain. (b) Give the infinitesimal rates of this chain. (c) Show that this chain is time reversible, and find the limiting probabilities. Sep 15 2014 06:32 AM

 

Solution ID:608884 | This paper was updated on 26-Nov-2015

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