Analytical models are widely applied in the world of mining engineering to analyze and assess machinery systems of the shovel-truck type based on models of queuing theory. A significant characteristic of these models, according to, among others, Kopocin´ska (1968), Barnes et al. (1979), Barbaro and Rosenshine (1986), Carmichael (1987) and Fabian (1989), is that the number of operating machines is assumed to be constant. This is contrary to operational practice. Czaplicki (2002, 2004, 2004/2005 and 2006) presented a different solution to the problem of the machinery system size accomplishing its task in a given moment of time. In the cited papers, the following is emphasized repeatedly: ‘the number of machines in work state is a random variable’. There is no doubt that the identification of factors inf luencing the probability distribution of this random variable is interesting from both theoretical and practical points of view. As Czaplicki states (2006) ‘identification of the probability distribution of the number of machines in work state gives a basis for trustworthy research-analysis and estimation of efficiency1 of the machinery system. This probability distribution has an inf luence on the values of most measures of system performance.’ Therefore, when commencing modelling in this chapter, the focus will be on the construction of this probability distribution. During modelling, various properties of the system will be investigated, creating a comprehensive analysis of it.