A numerical approach to cyclic-service queueing models

TLDR: In this article, an iterative numerical technique for the evaluation of queue length distributions is applied to multi-queue systems with one server and cyclic service discipline with Bernoulli schedules.

Abstract: An iterative numerical technique for the evaluation of queue length distributions is applied to multi-queue systems with one server and cyclic service discipline with Bernoulli schedules. The technique is based on power-series expansions of the state probabilities as functions of the load of the system. The convergence of the series is accelerated by applying a modified form of the epsilon algorithm. Attention is paid to economic use of memory space. The technique is based on power-series expansions of the state probabilities as functions of one parameter (the traffic intensity) of the systems. The coefficients of these power series can be recursively calculated for a large class of multi-queue models. The coefficients of the power-series expansions of the moments of the queue length distributions follow directly from those of the state probabillities. In most instances a bilinear transformation ensures convergence of the power series over the whole range of traffic intensities for which the system is stable. We have introduced in Blanc (2,3) extrapolations of the coefficients of the power series in order to accelerate the convergence of the series. One of these extrapolations will be combined with the epsilon algorithm (cf. Brezinski (6), Wynn (13)) in the present paper. The advantages of the present technique are that quantities are calculated iteratively, that it is relatively easy to compute additional terms of the power series in order to increase accuracy, that algorithms for accelerating the convergence of sequences can be applied, and that, once the coefficients of the

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Tilburg University
A numerical approach to cyclic-service queueing models
Blanc, J.P.C.
Publication date:
1988
Link to publication in Tilburg University Research Portal
Citation for published version (APA):
Blanc, J. P. C. (1988).
A numerical approach to cyclic-service queueing models
. (Research memorandum /
Tilburg University, Department of Economics; Vol. FEW 312). Unknown Publisher.
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A NUMERICAL
APPROACH
TO
CYCLIC-SERVZCE
QUEUEING MODELS
J.P.C.
Blanc
FEW 312

A
numerical approach
to
cyclic-service queueing models
J.P.C.
Blanc
Tilburg
University,
Eaculty
of
Economics
P.O.
Box
90153.
5000
LE
Tilburg,
The
Netherlands
Abstract
An
iterative numerical
technique
for the
evaluation of queue length
dis-
tributions
is
applied
to
multi-queue
systems
with
one
server and
cyclic
service
discipline with
Bernoulli
schedules.
The technique is based
on
power-series
expansions
of
the
state
probabilities
as
functions
of
the
load
of
the
system.
The convergence of
the
series
is
accelerated
by
apply-
ing
an
adapted
form
of
the
epsilon
algorithm.
Attention
is
paid
to
eco-
nomic
use of
inemory
space.
Keywords:
power-series
algorithm,
traffic
intensity,
waiting
time,
epsilon
algorithm,
memory
space.