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Update statistics in conservative parallel-discrete-event simulations of asynchronous systems.

A Kolakowska1, M A Novotny, Per Arne Rikvold

  • 1Department of Physics and Astronomy and the ERC Center for Computational Sciences, P.O. Box 5167, Mississippi State, Mississippi 39762-5167, USA. alicjak@bellsouth.net

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

We developed a model for parallel processing elements, revealing a connection between processor utilization and virtual time interface structure. This leads to a theoretical lower bound for computational speedup in asynchronous systems.

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Area of Science:

  • Computer Science
  • Theoretical Computer Science
  • Parallel Computing

Background:

  • Modeling asynchronous parallel processing systems is crucial for understanding computational performance.
  • Conservative update algorithms govern state transitions in many distributed systems.
  • The concept of virtual time surfaces is used to analyze system dynamics.

Purpose of the Study:

  • To model the performance of an ideal closed chain of L parallel processing elements.
  • To establish a connection between processor utilization and the microscopic structure of the virtual time interface.
  • To derive the theoretical probability distribution of updates and a lower bound for computational speedup.

Main Methods:

  • Developed a model for a closed chain of L asynchronous processing elements.

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  • Utilized a generic conservative algorithm for state updates.
  • Analyzed the growth of a virtual time surface and its relation to utilization and interface width.
  • Employed statistical methods to count surface-configuration classes.

    • Main Results:

    • Established an explicit connection between processor utilization and the microscopic structure of the virtual time interface.
    • Derived the theoretical probability distribution of updates within an approximate model.
    • Determined a theoretical lower bound for computational speedup: s=(L+1)/4 for L>=4.

    Conclusions:

    • The study provides analytical methods for computing microscopic interface properties, complementing continuum approaches.
    • The findings offer insights into the performance limits of asynchronous parallel processing systems.
    • The derived speedup bound is valuable for optimizing parallel computation.