Theoretical mean-variance relationship of IP network traffic based on ON/OFF model

Abstract

Mean-variance relationship (MVR), nowadays agreed in power law form, is an important function. It is currently used by traffic matrix estimation as a basic statistical assumption. Because all the existing papers obtain MVR only through empirical ways, they cannot provide theoretical support to power law MVR or the definition of its power exponent. Furthermore, because of the lack of theoretical model, all traffic matrix estimation methods based on MVR have not been theoretically supported yet. By observing both our laboratory and campus network for more than one year, we find that such an empirical MVR is not sufficient to describe actual network traffic. In this paper, we derive a theoretical MVR from ON/OFF model. Then we prove that current empirical power law MVR is generally reasonable by the fact that it is an approximate form of theoretical MVR under specific precondition, which can theoretically support those traffic matrix estimation algorithms of using MVR. Through verifying our MVR by actual observation and public DECPKT traces, we verify that our theoretical MVR is valid and more capable of describing actual network traffic than power lawMVR.