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##

Approximations for multiserver systems with multiple priority classes

We first introduce approximations for the mean delay in an
M/GI/ queue with priority classes (class jobs have
preemptive priority over jobs of classes to for
). The abovementioned BB
approximation was originally derived for exponential job size
distributions [33] and was later applied to general job
size distributions [23]. The BB approximation is the
only (reasonable) approximation, for general job size distributions and
for an arbitrary number of priority classes, that exists in the
literature. Mitrani and King have proposed an approximation that
works for exponential job size distributions and for an arbitrary
number of priority classes [129], and this approach is
also used by Nishida [140]. We refer to this approximation
as MK-N. The MK-N approximation is defined and used only for
exponential job size distributions, since MK-N requires an analysis of a multiserver queue
with two priority classes, and an exact or nearly exact analysis has been known only
for exponential job size distributions.
Our analysis of an M/PH/ queue with multiple priority classes via DR allows us to
extend MK-N to PH job size distributions.
We refer to the new approximation as DR-A. Below, we provide more details of the three approximations.

**Subsections**

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** Contents**
Takayuki Osogami
2005-07-19