Unformatted text preview: rate Î» . Suppose that whether or not a newly arriving customer joins the queue is determined randomly, according to the following scheme: Pr[New customer joins queue  n customers already in system] = 1 n + 1 . Hence, a new customer will not join the system with probability n n +1 . If the pump service time is exponential with rate Î¼ , show that the limiting distribution of the number of customers at the gas station is Poisson distributed with rate Î» Î¼ ....
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 Spring '09
 RESNIK
 Probability theory, Markov chain, timeÂ MarkovÂ Chains, Engineering Stochastic Processes, newly arriving customer, pump service time

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