Computing transient and steady-state distributions in pollingmodels by numerical transform inversion
Choudhury, G.L.; Whitt, W.
Communications, 1995. ICC apos;95 Seattle, apos;Gateway to Globalizationapos;, 1995 IEEE International Conference on
Volume 2, Issue , 18-22 Jun 1995 Page(s):803 - 809 vol.2
Digital Object Identifier 10.1109/ICC.1995.524214
Summary:We show that probability distributions of performance measures in
a large class of polling models can be effectively computed by
numerically inverting transforms (generating functions and Laplace
transforms). We develop new efficient iterative algorithms for computing
the transform values and then use the Fourier-series method to perform
the inversion. We also use this approach to compute moments. The
algorithms apply to the transient behavior of stationary or
nonstationary models as well as to the steady-state behavior of
stationary models. Our main focus is on computing exact tail
probabilities, but even for mean waiting times, our algorithm is faster
than previous algorithms for large models. The computational complexity
of our algorithm is O(Nα) for computing performance
measures at one queue and O(N1+α) for computing
performance measures at all queues, where N is the number of queues and
α is typically between 0.6 and 0.8. We demonstrate effectiveness
by computing performance measures in an asymmetric 1000-queue system
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