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Factorized time-dependent distributions for certain multiclass queueing networks and an application to enzymatic

W H Mather1, J Hasty1, L S Tsimring1

  • 1BioCircuits Institute, University of California, San Diego, USA.

Queueing Systems
|March 6, 2014
PubMed
Summary

We discovered a factorized form for multiclass queueing networks, simplifying complex queue-length distribution calculations. This method reduces multiclass problems to simpler single-class queueing network analyses, aiding biological system modeling.

Keywords:
CorrelationDimension reductionEnzymatic processingHomogeneous Kelly-type stationsIntracellular networksMulticlass queueing networkProduct formRenegingState-dependent routingState-space collapseStationary distributionUltrasensitivity of signal propagation

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Area of Science:

  • Operations Research
  • Applied Probability
  • Biomathematics

Background:

  • Multiclass queueing networks are prevalent in biological systems.
  • Analyzing time-dependent queue-lengths in these networks is computationally challenging.
  • Existing methods struggle with the complexity of multiple interacting queues.

Purpose of the Study:

  • To develop a simplified method for computing time-dependent queue-length distributions in multiclass queueing networks.
  • To demonstrate the applicability of this method in biological contexts.
  • To reduce the computational complexity of queueing network analysis.

Main Methods:

  • Derivation of a factorized form for multiclass queue-length distributions.
  • Reduction of multiclass queueing problems to single-class equivalents.
  • Application of the derived method to an enzymatic processing network model.

Main Results:

  • A factorized form for time-dependent distributions of multiclass queue-lengths was established.
  • The computational problem was successfully reduced to analyzing related single-class queueing networks.
  • The method's utility was demonstrated through an enzymatic processing network example.

Conclusions:

  • The factorized form provides a significant simplification for analyzing multiclass queueing networks.
  • This approach offers a powerful tool for modeling biological systems with queueing dynamics.
  • The findings facilitate more efficient computation of queue-length distributions in complex networks.