With the increase in computing power and software engineering in the past years computer based stochastic discrete-event simulations have become very commonly used tool to evaluate performance of various, complex stochastic systems (such as telecommunication networks). It is used if analytical methods are too complex to solve, or cannot be used at all. Stochastic simulation has also become a tool, which is often used instead of experimentation in order to save money and time by the researchers. In this thesis, we focus on the statistical correctness of the final estimated results in the context of steady-state simulations performed for the mean analysis of performance measures of stable stochastic processes. Due to various approximations the final experimental coverage can differ greatly from the assumed theoretical level, where the final confidence intervals cover the theoretical mean at much lower frequency than it was expected by the preset theoretical confidence level. We present the results of coverage analysis for the methods of dynamic partially-overlapping batch means, spectral analysis and mean squared error optimal dynamic partially-overlapping batch means. The results show that the variants of dynamic partially-overlapping batch means, that we propose as their modification under Akaroa2, perform acceptably well for the queueing processes, but perform very badly for auto-regressive process. We compare the results of modified mean squared error optimal dynamic partially-overlapping batch means method to the spectral analysis and show that the methods perform equally well.