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Comparing DRA with BB and MKN
Figure 4.7:
Comparison of DRA, MKN, and BB approximations for M/PH/2 with 4
priority classes
with
,
,
, and
, as a function of .
Here, the squared coefficient of variability of the job size distributions
are (top two rows) or (bottom two rows) for all classes. Load is balanced among the classes.
Note that MKN does not appear for ,
because the error is beyond the scale of the graphs for most values of .
Comparison of approximations for M/M/2 with 4 priority classes ()
Comparison of approximations for M/PH/2 with 4 priority classes ()

We now evaluate the accuracy of DRA,
BB, and MKN. In all figures,
we assume servers and priority classes. We consider
both the case where each priority class has an exponential job
size distribution (; top half of Figure 4.7)
and the case of twophase PH job size distributions with (bottom
half of Figure 4.7)^{4.3}. Each class may have a
different mean job size, and these are chosen to vary over a large
range, determined by parameter . Specifically, the mean job size of
class is set
, where
. Thus,
implies small high priority jobs. We equalize the load between
the classes, i.e.
, where is
the load of class . With these settings, the error in mean delay is evaluated for each class of
jobs, where the error of an approximation is defined as follows:
Thus, positive error means overestimation
and negative error means underestimation of the approximation.
Simulation is kept running until the simulation error becomes less
than 1% with probability 0.95 (see Section 3.9 for
more technical details of our simulation).
In evaluating the BB and MKN approximations, we use accurate methods
known to compute their components. For example, BB relies on knowing
the mean delay for the M/PH//FCFS queue. We compute this delay
precisely for the PH job size distribution using matrix analytic
methods. MKN relies on being able to analyze the case of two
priority classes (since classes are reduced to two). We analyze
the two priority class case in MKN using DR. We first discuss the accuracy of
MKN and DRA, and then discuss the accuracy of BB.
Subsections
Next: The MKN and DRA
Up: New approximations for many
Previous: New approximation: DRA
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Takayuki Osogami
20050719