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Unformatted text preview: Version:4/22/2011 ISyE 3232 H. Ayhan & J. Dai Homework 13 1. Consider a system having two independent M/M/ 1 queueing stations, each with its own wait- ing line. Let the arrival rate to each station be λ/ 2 and the service rate of each server be μ . We now pool two stations together and thus form an M/M/ 2 queueing system with one waiting line. The arrival rate to the pooled system is therefore, λ , and the service rate of each server is μ . Assuming λ < 2 μ , compare N and N q for these two systems. 2. 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 has3....
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This note was uploaded on 01/16/2012 for the course ISYE 3232 taught by Professor Billings during the Spring '07 term at Georgia Institute of Technology.
- Spring '07