A deep understanding of the queuing performance of wireless networks is essential for the advancement of future wireless communications. The stochastic nature of wireless channels in general gives rise to a time varying transmission rate. In such an environment, interference is increasingly becoming a key constraint. Obtaining an expressive model for offered service of such channels has major implications in the design and optimization of future networks. However, interference channels are not well-understood with respect to their higher layer performance. The particular difficulty for handling interference channels arises from the superposition of random fading processes for the signals of the transmitters involved (i.e., for the signal of interest and for the signals of the interferers). Starting from the distribution of the signal-to-interference-plus-noise ratio (SINR), we derive a statistical characterization of the underlying service process in terms of its Mellin transform. Then, we adapt a recent stochastic network calculus approach for fading channels to derive measures of the queuing performance of single- and multi-hop wireless interference networks. Special cases of our solution include noise-limited and interference-limited systems. A key finding of our analysis is that for a given average signal and average sum interference power, the performance of interfered systems not only depends on the relative strength of the sum interference with respect to the signal-of-interest power, but also on the interference structure (i.e., the number of interferers) as well as the absolute levels.