Regeneration Cycles Dependence in Confidence Estimation by Splitting
Alexandra V. Borodina (Karelian Research Centre of Russian Academy of Science, Russia)
The problem of confidence estimation of a high load probability 
in M/G/1 and GI/G/1 systems is considered.
In the previous research a special speed-up simulation technique
based on combination of splitting and regenerative approach has been
proposed for the consistent (point) estimation of the probability
.
Since the queue-size process in a M/G/1 system (and the workload process is GI/G/1 queue) is non-Markovian, then a dependence between regeneration cycles obtained by splitting appears.
It follows from the splitting procedure, that the regeneration
cycles turns out to be at most 
-dependent, where
constant is defined as
and 
is the number of split trajectories at
the 
-th threshold. (
is the number of thresholds.)
Therefore, we may use a Central Limit Theorem for -dependable random
variables to construct confidence interval for . Furthermore, the
dependence of on the shape (and width)
of the confidence interval on constant is investigated.
