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Computing various performance measures
So far, our focus has been on computing the stationary probabilities
in the RFB/GFB process. In this section, we discuss how the
stationary probabilities can be used to compute other performance
measures. In Section 3.8.1, we consider the distribution of
the number of jobs in the system and its moments. In
Section 3.8.2, we consider the distribution of response time
and its moments. Since the computation of these performance measures
depends on particular multiserver systems and details of modeling, we
will illustrate the approach via an example in the case of an M/M/2 queue
with two preemptive priority classes (recall Figure 3.3),
and briefly discuss how this can be applied to other multiserver systems.
Figure 3.28:
Markov chains whose stationary probabilities are computed via DR
in the analysis of an M/M/2 queue with two preemptive priority classes.

Figure 3.28 shows the Markov chains whose stationary
probabilities are computed via DR in the analysis of an M/M/2 queue
with two preemptive priority classes. Figure 3.28(a) shows
the background process, where state (level) corresponds to the
state with high priority jobs for .
Let
be the stationary probability in
state (level) of the background process.
Observe that
is the probability that there are
high priority jobs in the system for .
Figure 3.28(b) shows the 1D Markov chain reduced from the
2D Markov chain (FB process), where level consists of the states
with low priority jobs for .
Let
be the stationary probability vector in
level of the 1D Markov chain shown in Figure 3.28(b).
Observe that
is the probability that
there are low priority jobs in the system for .
Subsections
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Takayuki Osogami
20050719