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Power-law and exponential tails in a stochastic priority-based model queue.

G Grinstein1, R Linsker

  • 1IBM T. J. Watson Research Center, P. O. Box 218, Yorktown Heights, New York 10598, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary
This summary is machine-generated.

This study analyzes a stochastic queueing model with continuous priorities. We found waiting times follow power laws, P(tau) ~ tau(-3/2) for micro<=lambda and P(tau) ~ tau(-5/2)exp[...] for micro>lambda.

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Area of Science:

  • Operations Research
  • Applied Probability
  • Queueing Theory

Background:

  • Stochastic queueing models are fundamental in performance analysis.
  • Understanding task waiting times is crucial for system efficiency.
  • Continuous-valued priorities introduce complex dynamics.

Purpose of the Study:

  • Derive exact asymptotic results for waiting times in a specific queueing model.
  • Characterize the waiting time distribution under different arrival and execution rates.
  • Provide a theoretical basis for empirical observations.

Main Methods:

  • Mathematical derivation of asymptotic behavior.
  • Analysis of a stochastic queueing model with continuous priorities.
  • Asymptotic analysis of probability distributions.

Main Results:

  • The waiting time distribution P(tau) follows a power law P(tau) ~ tau(-3/2) when execution rate (micro) is less than or equal to arrival rate (lambda).
  • For micro > lambda, the distribution is P(tau) ~ tau(-5/2)exp[-(sqrt[micro]-sqrt[lambda])2tau].
  • These results provide exact asymptotic formulas.

Conclusions:

  • The derived asymptotic formulas accurately describe waiting time distributions in this model.
  • The behavior of waiting times is highly dependent on the ratio of execution to arrival rates.
  • Theoretical results confirm and extend previous empirical findings.