Long range dependence in network traffic and the closed loop behaviour of buffers under adaptive window control

Abstract

We consider an Internet link carrying http-like traffic, i.e., transfers of finite volume files arriving at random time instants. These file transfers are controlled by an adaptive window protocol (AWP); an example of such a protocol is TCP. We provide analysis for the auto-covariance function of the AWP-controlled traffic into the link's buffer; this traffic, in general, cannot be represented by an on-off process. The analysis establishes that, for TCP-controlled transfer of Pareto-distributed file sizes with infinite second moment, the traffic into the link buffer is long range-dependent (LRD). We also develop an analysis for obtaining the stationary distribution of the link buffer occupancy under an AWP-controlled transfer of files sampled from some distribution. For any AWP, the analysis provides us with the Laplace-Stieltjes transform (LST) of the distribution of the link buffer occupancy process in terms of the functions defining the AWP and the file size distribution. The analysis also provides a necessary and a sufficient condition for the finiteness of the mean link buffer content; these conditions again have explicit dependence on the AWP used and the file size distribution. This establishes the sensitivity of the buffer occupancy process to the file size distribution. Combining the results from the above analyses, we provide various examples in which the closed loop control of an AWP results in finite mean link buffer occupancy even though the file sizes are Pareto-distributed (with infinite second moment), and the traffic into the link buffer is long range-dependent (with Hurst parameters which would suggest an infinite mean queue occupancy under open loop analysis). We also study the effect of window reductions due to active queue management and find that window reductions lead to further lightening of the tail of buffer occupancy distribution. The significance of this work is three-fold: (i) by looking at the window evolution as a function of the amount of data served and not as a function of time, this work provides a new framework for analysing various processes related to the link buffer under AWP-controlled transfer of files with a general file size distribution; (ii) it indicates that the buffer behaviour in the Internet may not be as poor as predicted from an open loop analysis of a queue fed with LRD traffic; and (iii) it shows that the buffer behaviour (and hence the throughput performance for finite buffers) is sensitive to the distribution of file sizes.