Closed loop analysis of the bottleneck buffer under adaptive window controlled transfer of http-like traffic

Abstract

An Internet link carrying http-like traffic, i.e., transfer of finite volume files starting at random time instants is considered. These file transfers are controlled by an adaptive window protocol (AWP); an example of such a protocol is TCP. We provide an analysis for the auto-covariance function of the AWP controlled traffic into the link's buffer; this traffic, in general, is not an on-off process. The analysis establishes that, for 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. The analysis provides a necessary and a sufficient condition for the finiteness of the mean link buffer content; these conditions 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 an example 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. The significance of this work is threefold: (i) it provides a 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.