Fast solvers for queueing systems with negative customers

You Wei Wen*, Wai Ki Ching, Kwok Po NG

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

2 Citations (Scopus)

Abstract

In this paper, we are interested in solving queueing systems having Poisson batch arrivals, exponential servers and negative customers. Preconditioned Conjugate Gradient (PCG) method is applied to solving the steady-state probability distribution of the queueing system. Preconditioners are constructed by exploiting near-Toeplitz structure of the generator matrix and the Gohberg-Semumcul formula. We proved that the preconditioned system has singular values clustered around one. Therefore Conjugate Gradient (CG) methods when applied to solving the preconditioned system, we expect fast convergence rate. Numerical examples are given to demonstrate our claim.

Original languageEnglish
Title of host publicationProceedings of VALUETOOLS
Subtitle of host publication1st International Conference on Performance Evaluation Methodologies and Tools
DOIs
Publication statusPublished - 2006
EventVALUETOOLS: 1st International Conference on Performance Evaluation Methodologies and Tools - Pisa, Italy
Duration: 11 Oct 200613 Oct 2006

Publication series

NameACM International Conference Proceeding Series
Volume180

Conference

ConferenceVALUETOOLS: 1st International Conference on Performance Evaluation Methodologies and Tools
Country/TerritoryItaly
CityPisa
Period11/10/0613/10/06

Scopus Subject Areas

  • Software
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Networks and Communications

User-Defined Keywords

  • Gohberg-semencul formula
  • Negative customer
  • Preconditioned conjugate gradient method
  • Preconditioners
  • Queueing systems

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