Few theoretical results have been obtained in the literature for the effects of dependencies between random variables on the performance of queueing systems. This thesis aims at investigating this issue via simulation. Several dependencies are studied in detail, including dependencies between interarrival times, between interarrival time and service time, between service times and dependencies between different stages in networks of queues. We define several classes of dependent random variables and study their correlation coefficients, then we apply them to single and multiple station service systems. Comparisons with the independent case, for which the explicit form solution are available, are made and characterized by figures. The main contribution of this thesis is that it disproves the monotonicity properties of effect of dependencies on system performance in both single and multiple service stations queueing systems. These results may be helpful in evaluating the performance of both telecommunication and manufacturing systems.