Defining means and methods designed to ensure the quality of service (QoS mechanisms), which is the objective of the first part of this paper, involves a series of analytical or experimental modeling activities (for example, by simulation) and analysis which, in turn, involve various mathematical disciplines, such as probability theory and statistics, in order to determine how to act, considering the factors that influence the quality of service. Having a generous theoretical support, each of these mentioned activities and instruments is a separate subject, the exposure of which can be found in the following two parts of this paper. This is the Part II, which aims at presenting the basic analytical tools used in the description of random phenomena, and the Part III, dealing with the specific aspects of telecommunication services, regarding the modeling and analysis processes for their quality.