ISyE 4803 Ayhan Summer 2010 Summary: ISyE 4803 Ayhan Summer 2010 Homework 1 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 p1 = 10% probability going back to station 1 for rework and 1 - p1 probability continuing onto station 3. After being processed at station 3, a job has p2 = 5% probability going back to station 1, p3 = 10% probability going back to station 2, and 1 - p2 - p3 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 m1 = 0.8, m2 = 0.70 and m3 = 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 p1 to 5%. Answer (1c) again. What story can you tell? 2. Consider the production system in Problem 1 with following modification: p1 = 10%, p2 = Collections: Engineering