Suppose that the service rates at the three stands

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Unformatted text preview: ribution. 4.35. Customers arrive at a carnival ride at rate . The ride takes an exponential amount of time with rate µ, but when it is in use, the ride is subject to breakdowns at rate ↵. When a breakdown occurs all of the people leave since they know that the time to fix a breakdown is exponentially distributed with rate . (i) Formulate a Markov chain model with state space { 1, 0, 1, 2, . . .} where 1 is broken and the states 0, 1, 2, . . . indicate the number of people waiting or in service. (ii) Show that the chain has a stationary distribution of the form ⇡ ( 1) = a, ⇡ (n) = b✓n for n 0. 4.36. Customers arrive at a two-server station according to a Poisson process with rate . Upon arriving they join a single queue to wait for the next available server. Suppose that the service times of the two servers are exponential with rates µa and µb and that a customer who arrives to find the system empty will go to each of the servers with probability 1/2. Formulate a Markov chain model for this system with state space {0, a, b, 2, 3, . . .} where the s...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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