Modeling and analysis of adaptive window controlled randomly arriving file transfers in Internets

Abstract

The Internet carries predominantly elastic traffic generated by applications such as email, web transfers, and file transfers, and the bandwidth sharing between such sessions is controlled by the Transmission Control Protocol (TCP). Dimensioning, designing, and planning of IP networks are important problems for which satisfactory solutions are not yet available. Many network operators and Internet Service Providers (ISPs) dimension their networks by trial and error. An important measure of performance for elastic transfers is the transfer throughput. Hence, developing performance models that can be used to calculate the throughputs obtained by TCP?controlled elastic sessions will assist in bandwidth dimensioning and traffic engineering. It is also useful to understand the characteristics of traffic on Internet links and the behaviour of router buffers for performance evaluation, measurement, and control purposes. Most studies of implicit or explicit feedback control of elastic sessions consider only persistent sources with an infinite backlog of data to send. In real applications, however, the TCP connections over a link are short?lived; a new TCP connection starts, transmits a finite number of packets (from a file in the web server), and then closes the connection. In this thesis, we address the following problems: (i) Analytical models for predicting the throughput performance of TCP?controlled short?lived (or web?like) transfers over a bottleneck link, and (ii) The closed?loop characterization of network traffic and buffer behaviour under TCP?controlled finite?volume transfers.

Part I — Throughput Models for TCP?Controlled Finite File Transfers The first part of this thesis is about analytical models for calculating the average bandwidth shares obtained by TCP?controlled finite?volume file transfers that arrive randomly and share a single (bottleneck) link. Owing to the complex nature of TCP’s congestion/flow control algorithm, a single model does not work well for all combinations of system parameters (mean file size, link capacity, and propagation delay). We propose two models, develop their analyses, and identify the regions where they apply:

TCP?PS Model - derived from a detailed analysis of TCP’s additive?increase multiplicative?decrease (AIMD) adaptive window mechanism. The analysis accounts for:

session arrivals and departures, finite link buffers, and a general file?size distribution (approximated as a mixture of exponentials). It is essentially a Processor Sharing (PS) model with a time?varying service rate.

Rate?Limited PS (RL?PS) Model - a simple modification of the PS model that accounts for large propagation delays. This model can also handle general file?size distributions.

We show that the TCP?PS model converges to the standard PS model as the propagation delay approaches zero. However, the PS model provides poor throughput estimates unless the propagation delay is very small. The key parameters affecting throughput are observed to be:

bandwidth–delay product (BDP), file?size distribution, link buffer size, and traffic intensity.

Extensive numerical comparisons between analytical and simulation results show:

TCP?PS is accurate when BDP is small compared to the mean file size. RL?PS is accurate when BDP is large compared to the mean file size.

We also provide results on how the PS model can be used for modelling TCP throughput in an Internet path consisting of multiple links.

Part II — Closed?Loop Traffic and Buffer Behaviour In the second part of the thesis, we consider a link carrying web?like traffic where finite?volume file transfers start at random time instants. These file transfers are controlled by an Adaptive Window Protocol (AWP), such as TCP. We assume that the link buffer implements a per?flow fair scheduling mechanism. For this scenario, we develop an analysis for the auto?covariance function of AWP?controlled traffic into the link buffer. This traffic is generally not an on–off process. The analysis shows that when file sizes are Pareto distributed with infinite second moment, the closed?loop traffic into the link buffer becomes long?range dependent (LRD) under TCP?controlled transfers. We also derive the stationary distribution of the buffer occupancy under AWP?controlled transfers of files with arbitrary size distributions. We find that under TCP’s congestion avoidance mechanism, the tail of the stationary buffer occupancy distribution is lighter than what would be predicted by an open?loop queue fed with LRD traffic. The analysis provides necessary and sufficient conditions for the finiteness of the mean link?buffer content, and these conditions explicitly depend on:

the AWP (e.g., TCP), and the file?size distribution.

Combining our results, we provide an example where:

closed?loop AWP control results in finite mean buffer occupancy, file sizes are Pareto distributed (with infinite second moment), and traffic into the link buffer is LRD.

Significance of the Work The importance of this investigation is threefold:

It provides a unified framework for analysing processes related to link?buffer behaviour under AWP?controlled file transfers with general file?size distributions. It shows that buffer behaviour in a real Internet may be significantly better than predicted by traditional open?loop analysis with LRD inputs. It demonstrates that buffer behaviour-and hence throughput-depends sensitively on file?size distributions.