STOCHASTICS SEMINAR :: Asymptotic results for the stationary distribution of a production system: a work in progress

Event Details
  • Date/Time:
    • Tuesday November 21, 2006 - Monday November 20, 2006
      10:00 am - 11:00 pm
  • Location: Executive Classroom (Main Building 228)
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Contact
Barbara Christopher
Industrial and Systems Engineering
Contact Barbara Christopher
404.385.3102
Summaries

Summary Sentence: STOCHASTICS SEMINAR :: Asymptotic results for the stationary distribution of a production system: a work in progress

Full Summary: STOCHASTICS SEMINAR :: Asymptotic results for the stationary distribution of a production system: a work in progress

Consider a production system where two types of jobs, $a$ and $b$ arrive at a central buffer according to independent Poisson processes with rates $lambda_a$ and $lambda_b$, respectively. Machines $m_1$ and $m_2$ select jobs from the central buffer when they are idle. When machine $m_1$ becomes idle, it takes the job from the head of the line, regardless of type, and serves it at rate $mu_1$. When machine $m_2$ becomes idle, it takes the earliest arrival among the type $a$ jobs and serves it at rate $mu_2$. Thus, the queue discipline is FCFS subject to the restriction that machine $m_2$ only processes type $a$ jobs. We derive rough and exact asymptotic results for the steady state behavior of this production system. For some parameter values, the fluid limit of the most likely approach to the rare event is nonlinear.

Joint work with Ivo Adan and David McDonald

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Status
  • Created By: Barbara Christopher
  • Workflow Status: Published
  • Created On: Oct 8, 2010 - 7:32am
  • Last Updated: Oct 7, 2016 - 9:52pm