Homework 8

Homework 8 - rate ╬ Suppose that whether or not a newly...

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ORIE3510 Introduction to Engineering Stochastic Processes Spring 2010 Homework 8: Continuous Time Markov Chains Due 2:30pm, ( Friday! ) April 9, 2010 (drop box) In all questions, be sure to give the justification for your answers. There is one problem worth 100 points. This is a short assignment, and you have until April 9 to turn it in. However, on Wednesday April 7, we will post homework 9 which will be of the usual length. Make sure you budget your time accordingly! Problem 1 Consider a single-pump gas station to which customers arrive according to a Poisson process with
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Unformatted text preview: rate ╬╗ . 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 ╬╝ , show that the limiting distribution of the number of customers at the gas station is Poisson distributed with rate ╬╗ ╬╝ ....
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  • Spring '09
  • Probability theory, Markov chain, time┬áMarkov┬áChains, Engineering Stochastic Processes, newly arriving customer, pump service time

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