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\documentclass{acmabs}

\begin{document}

\Journal{Journal of the ACM}

\refkey{ChoudhuryLW95}

\title{Calculating Normalization Constants of Closed Queueing Networks by
  Numerically Inverting Their Generating Functions}

\author{Gagan~L. Choudhury \and Kin~K. Leung \and Ward Whitt}

\Month{September}

\Year{1995}

\Volume{42}

\Number{5}

\note{To appear}

\maketitle

\begin{abstract}

A new algorithm is developed for calculating normalization constants (partition
  functions) and moments of product-form steady-state distributions of closed
  queueing networks and related models. The essential idea is to numerically
  invert the generating function of the normalization constant and related
  generating functions appearing in expressions for the moments. It is known
  that the generating function of the normalization constant often has a
  remarkably simple form, but numerical inversion evidently has not been
  considered before. For $p$-dimensional transforms, as occur with queueing
  networks having $p$ closed chains, the algorithm recursively performs $p$
  one-dimensional inversions. The required computation grows exponentially in
  the dimension, but the dimension can often be reduced by exploiting
  conditional decomposition based on special structure. For large populations,
  the inversion algorithm is made more efficient by computing large sums using
  Euler summation. The inversion algorithm also has a very low storage
  requirement. A key ingredient in the inversion algorithm is scaling. An
  effective static scaling is developed for multichain closed queueing networks
  with only single-server and (optionally) infinite-server queues. An important
  feature of the inversion algorithm is a self-contained accuracy check, which
  allows the results to be verified in the absence of alternative algorithms.

\end{abstract}

\begin{keywords}

performance analysis, closed queueing networks, product-form model,
  normalization constant, partition function, generating function, numerical
  transform inversion, scaling, dimension reduction, Euler summation

\end{keywords}

\end{document}
