Estimation Techniques
131
Alternatively, we can run one very long simulation. Allow first the simulation to
reach its steady state, and then collect the first sample of observations. Subsequently,
instead of terminating the simulation and starting all over again, we extend the simulation
run in order to collect the second sample of observations, then the third sample and so on.
The advantage of this method is that it does not require the simulation to go through a
transient period for each sampling period. However, some of the observations that will be
collected at the beginning of a sampling period will be correlated with observations that
will be collected towards the end of the previous sampling period.
The replication method appears to be similar to the batch means approach.
However, in the batch means method, the batch size is relatively small and, in general,
one collects a large number of batches. In the above case, each sampling period is very
large and one collects only a few samples.
d.
Regenerative method
The
last
two
methods
described
above
can
be
used
to
obtain
independent
or
approximately independent sequences of observations. The method of independent
replications generates independent sequences through independent runs. The batch means
method generates approximately independent sequences by breaking up the output
generated in one run into successive subsequences which are approximately independent.
The regenerative method produces independent subsequences from a single run. Its
applicability, however, is limited to cases which exhibit a particular probabilistic
behaviour.
Let us consider a single server queue. Let t
0
, t
1
, t
2
,... be points at which the
simulation model enters the state where the system is empty. Such time instances occur
when a customer departs and leaves an empty system behind. Let t
0
be the instance when
the simulation run starts assuming an empty system. The first customer that will arrive
will see an empty system. During its service, other customers may arive thus forming a
queue. Let t
1
be the point at which the last customer departs and leaves an empty system.
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 Spring '10
 LAMBADARIS
 Normal Distribution, Probability theory, regeneration points, approximately independent sequences, time instances

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