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

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

Throughput Analysis of TCP in Multi-Hop Wireless Networks with IEEE 802.11 MAC

We consider the problem of modeling TCP over multi-hop wireless networks using the IEEE 802.11 protocol. By identifying suitable regeneration instants, we are able to apply the standard technique of regenerative processes to compute the long term average throughput achieved by a single TCP session. Simulation results show that the proposed model predicts the TCP throughput to a very high level of accuracy. We then discuss how to extend this model to more general situations

The Lightening Effect of Adaptive Window Control

We consider adaptive window (e.g., TCP) controlled transfer of http-like traffic (i.e., finite volume file transfers starting at random time instants) over a link, and develop an analysis for obtaining the stationary distribution of the link buffer occupancy. The significance of this work is that it provides a framework for analyzing the "closed-loop" behavior of the link buffer under adaptive window controlled transfer of files with a general file size distribution. We find that the tail of the stationary distribution of the buffer occupancy is lighter than may be expected from an open loop analysis. We also find that the tail of the buffer distribution is sensitive to the distribution of the file sizes, which provides insight into the sensitivity of TCP performance to file size distribution

Stochastic Models for Throughput Analysis of Randomly Arriving Elastic Flows in the Internet

This paper is ahnut analytical mndels fnr calculating the aver-age handwidth shares nhtained hy TCP cnntrnlled finite file transfers that arrive randnmly and share a single (bottleneck) link. Owing tn the complex nature nf the TCP cnngestinn cnntrnl algnrithm, a single mndel dries nnt wnrk well fnr all cnmhinatinns nf netwnrk parameters (i.e., mean file size, link capacity, and prnpagatinn delay). We prnpnse twn mndels, de-velnp their analyses, and identify the reginns nf their applicability. One mndel is nhtained frnm a detailed analysis nf TCP’s AIMD adaptive win-dnw mechanism; the analysis accnunts fnr sessinn arrivals and departures, and finite link buffers. It is essentially a Prncessnr Sharing (PS) mndel with time varying service rate; hence we call it TCP-PS. The nther mndel is a simple mndificatinn nf the PS mndel that accnunts fnr large prnpagatinn delays; we call this mndel Rate Limited-PS (RL-PS). The TCP-PS mndel analysis accnmmndates a general file size distrihutinn hy apprnximating it with a mixture nf expnnentials. The RL-PS mndel can he used fnr general file size distrihutinns. We shnw that the TCP-PS mndel cnnverges tn the standard PS mndel as the prnpagatinn delay apprnaches zern. We alsn nhserve that the PS mndel prnvides very pnnr estimates nf thrnughput unless the prnpagatinn delay is very small. We nhserve that the key parameters affecting the thrnughput are the handwidth delay prnduct (BDP), file size distrihutinn, the link buffer and the traffic intensity. Several numerical cnmparisnns between analytical and simulatinn re-sults are prnvided. We nhserve that the TCP-PS mndel is accurate when the BDP is small cnmpared tn the mean file size, and the RL-PS mndel wnrks well when the BDP is large cnmpared tn the mean file size.

Closed Loop Analysis of the Bottleneck Buffer under Adaptive Window Controlled Transfer of HTTP-Like Traffic

We consider an Internet link carrying http-like traffic, i.e., transfer of finite volume files starting 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 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

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

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 meanlink 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 AYR-controlled transfer of files with a general file size distribution; (ii) it indicates that the buffer behaviour in the Internet may not be as pooras predicted from an open loop analysis of a queue fed with LRD traffic; and (iii) it shows that the buffer behaviour (and hence thethroughput performance for finite buffers) is sensitive to the distribution of file sizes