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.