According to recent experimental evidence, the interaction between chromatin loops, which can be characterized by three factors-connection pattern, distance between regulatory elements, and communication form, play an important role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effect that addresses the question of how changes in these factors affect variability at the expression level in a systematic rather than case-by-case fashion. Here we make such an effort, based on a mechanic model that maps three fundamental patterns for two interacting DNA loops into a 4-state model of stochastic transcription. We first show that in contrast to side-by-side loops, nested loops enhance mRNA expression and reduce expression noise whereas alternating loops have just opposite effects. Then, we compare effects of facilitated tracking and direct looping on gene expression. We find that the former performs better than the latter in controlling mean expression and in tuning expression noise, but this control or tuning is distance-dependent, remarkable for moderate loop lengths, and there is a limit loop length such that the difference in effect between two communication forms almost disappears. Our analysis and results justify the facilitated chromatin-looping hypothesis.