13.07.Fall - p 3 = 10 probability going back to station 2...

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ISyE 3232 Stochastic Manufacturing and Service Systems Fall 2007 Professors Ayhan and Dai Homework 13 December 4, 2007 (Will not be collected,but you are expected to practice on these problems before test) 1. Consider a production system consisting of three single-server stations in series. Customer orders arrive at the system according to a Poisson process with rate 1 per hour. Each customer order immediate triggers a job that is released to the production system to be processed at station 1 first, and then at station 2. After being processed at station 2, a job has p 1 = 10% probability going back to station 1 for rework and 1 - p 1 probability continuing onto station 3. After being processed at station 3, a job has p 2 = 5% probability going back to station 1,
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Unformatted text preview: p 3 = 10% probability going back to station 2, and 1-p 2-p 3 probability leaving the production system as a finished product. Assume that the processing times of jobs at each station are iid, having exponential distribution, regardless of the history of the jobs. The average processing times at stations 1, 2 and 3 are m 1 = 0 . 8, m 2 = 0 . 70 and m 3 = 0 . 8 hours, respectively. (a) Find the long-run fraction of time that there are 2 jobs at station 1, 1 job at station 2 and 4 jobs at station 3. (b) Find the long-run average (system) size at station 3. (c) Find the long-run average time in system for each job. (d) Reduce p 1 to 5%. Answer 1(c) again. What story can you tell?...
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