STOCHASTICS SEMINAR SERIES -- Performance Measure Approximations for GI/GI/1 Queues with Reneging

Event Details
  • Date/Time:
    • Friday April 12, 2002
      3:00 pm - 12:00 am
  • Location: ISyE 304
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Contact
Barbara Christopher
Industrial and Systems Engineering
Contact Barbara Christopher
404.385.3102
Summaries

Summary Sentence: STOCHASTICS SEMINAR SERIES -- Performance Measure Approximations for GI/GI/1 Queues with Reneging

Full Summary: STOCHASTICS SEMINAR SERIES -- Performance Measure Approximations for GI/GI/1 Queues with Reneging

Models in which jobs renege arise in queueing contexts where jobs arrive with deadlines. Once a job's time-in-system exceeds its deadline, the job leaves the queue (and thereby reneges). One practical context which gives rise to such models is wireless networking. In this environment, certain packets of data (for example, location data) lose their value unless transmitted or received within a given time interval.

One model for the above situation is a GI/GI/1 queue in which jobs renege after an independent, generally distributed amount of time. For this model, neither steady-state nor transient performance measures can be computed analytically. When the arrival rate is close to the processing rate and reneging times are large, we develop performance measure approximations via both a reflected Ornstein-Uhlenbeck diffusion process and a reflected affine diffusion process. (An affine diffusion is one which has affine infinitesimal mean and variance.) We discuss the advantages and disadvantages of both approximations and perform simulations to evaluate their performance.

The approximations we suggest are rigorously justified by functional limit theorems for the workload process. Because such limit theorems do not automatically imply convergence of the corresponding steady-state distributions, we provide new methodology for establishing this convergence that leverages off existing functional limit theorems.

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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 - 7:43am
  • Last Updated: Oct 7, 2016 - 9:53pm