Unformatted text preview: they transient or recurrent? Is the MP irreducible? 1 2 2 Î» Î¼ 1 Î» Î¼ 2 A single class: { , 1 , 2 } = â‡’ Irreducible and Recurrent. (c) Determine the equilibrium distribution for this MP. Ï€ = 1 1 + 2 Î»/Î¼ 1 + 2 Î» 2 /Î¼ 1 Î¼ 2 Ï€ 1 = 2 Î» Î¼ 1 Ï€ Ï€ 2 = 2 Î» 2 Î¼ 1 Î¼ 2 Ï€ 2. Potential customers arrive at a fullservice, onepump gas station at a Poisson rate of 20 cars per hour. However, customers will only enter the station for gas if there are no more than two cars (including the one currently being attended to) at the pump. Suppose the amount of time required to service a car is exponentially distributed with a mean of ï¬ve minutes. (a) What fraction of the attendantâ€™s time will be spent servicing cars? 1Ï€ = 81 . 63% (b) What fraction of potential customers are lost? Ï€ 2 = 51 . 02% 1...
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 Fall '08
 Chisholm
 Probability, Probability theory, Personal computer, Minicomputer, requests

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