In this thesis we study the time-dependent behavior of queueing systems. The study is focused on the queueing systems: 1. the GI/G/1 system, 2. the GI/Hm/s system, 3. the Markovian Fluid Flow Model, the fluid flow model that is modulated by a Markov process, 4. the Semi-Markovian Fluid Flow Model, a generalization of the Markovian Fluid Flow Model. In general, the time-dependent behavior of queueing systems is much influenced by the initial server(s)’s work load. This leads us to consider the queueing systems with non-zero initial server(s)’s work load. In the GI/G/1 system and the GI/Hm/s system this means that in the beginning there exist a number of (special) customers to serve. In the last two systems, initially the buffer has non-zero content. The technique that is used to analyze the behavior of the queueing systems studied in this thesis is based on the Wiener-Hopf factorization. A brief discussion on the Wiener-Hopf factorization is given in chapter 2, where we also give the conditions on the existence of uniqueness of the factorization. In this chapter we also give some preliminaries that we need for the analysis in the rest chapters.