We propose a systematic approach to quantify the impact of nonuniform traffic on the performance of non-blocking switches with output queueing. We do so in the context of a simple queueing model where cells arrive to input ports according to independent Bernoulli processes, and are switched to an output port under a random routing mechanism. We give conditions on pairs of input rate vectors and switching matrices which ensure various stochastic comparisons for performance measures of interest. These conditions are formulated in terms of the majorization ordering while the comparison results are expressed in the strong and convex increasing orderings.