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The objective of this paper is to introduce self-similarity as a fundamental property exhibited by the bursty traffic between on-chip modules in typical MPEG-2 video applications. Statistical tests performed on relevant traces extracted from common video clips establish unequivocally the existence of self-similarity in video traffic. Using a generic tile-based communication architecture, we discuss the implications of our findings on on-chip buffer space allocation and present quantitative evaluations for typical video streams. We also describe a technique for synthetically generating traces having statistical properties similar to those obtained from real video clips. Our proposed technique speeds up buffer simulations, allows media system designers to explore architectures rapidly and use large media data benchmarks more efficiently. We believe that our findings open new directions of research with deep implications on some fundamental issues in on-chip networks design for multimedia applications.