Iterative methods for overflow queueing models I


*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

27 Citations (Scopus)


Markovian queueing networks having overflow capacity are discussed. The Kolmogorov balance equations result in a linear homogeneous system, where the right null-vector is the steady-state probability distribution for the network. Preconditioned conjugate gradient methods are employed to find the null-vector. The preconditioner is a singular matrix which can be handled by separation of variables. The resulting preconditioned system is nonsingular. Numerical results show that the number of iterations required for convergence is roughly constant independent of the queue sizes. Analytic results are given to explain this fast convergence.

Original languageEnglish
Pages (from-to)143-180
Number of pages38
JournalNumerische Mathematik
Issue number2
Publication statusPublished - Mar 1987
Externally publishedYes


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