## Title:

Engset-Model Based Method for Analysing Feedback-Based Protocols with Applications to Engineering Web Traffic over the Internet

## Authors:


D. P. Heyman              T. V. Lakshman               Arnold L. Neidhardt
Bellcore                  Bell Labs                    Bellcore
Red Bank NJ 07701          Holmdel, NJ 07733            Red Bank NJ 07701


Abstract:

Most of the studies of feedback-based flow and congestion control consider only persistent sources which always have data to send. However, with the rapid growth of Internet applications built on TCP/IP such as the World Wide Web and the standardization of traffic management schemes such as Available Bit Rate (ABR) in Asynchronous Transfer Mode (ATM) networks, it is essential to evaluate the performance of feedback-based protocols using traffic models which are specific to dominant applications. This paper presents a method for analysing feedback-based protocols with a Web-like input traffic where the source alternates between transfer" periods followed by think" periods.

Feedback-based protocols, such as TCP, slow down the sources upon detection of congestion (through packet loss in the case of TCP). The rate reduction upon congestion onset may trigger efficiency impairing effects in the protocol because the protocol may not track the available bottleneck link rate accurately. An example is the large window oscillations in TCP which impairs efficiency in the absence of sufficient buffering. Our model is a modification of the Engset model, which has no notion of feedback and no buffer, and congestion causes blocking. The key step is to represent the effect of the feedback protocol as a service-rate reduction for each source. If the feedback protocol were perfect, after onset of congestion, all the available capacity of the bottleneck link will be shared amongst the sources (with each source's allowed sending rate being reduced from its pre-congestion value) without any capacity loss. Since feedback protocols are not perfect unless there is no feedback delay, some of the bottleneck link capacity is lost. The amount of capacity loss is protocol specific. Also, the size of the buffer influences the amount of rate reduction (in our model the buffer size only appears in the efficiency calculations for the feedback protocol). This representation yields analytical tractability and gives the model the important {\em insensitivity} property: The steady-state probabilities for the number of transmitting sources depend only on the means of the transfer (file) sizes and the think times; other characteristics of the distributions for these random variables are irrelevant. Moreover, only the ratio of these two means enter the formulas.

Our adaptation of the Engset model allows for heterogenous sources that can have arbitrary distributions for the sizes of retrieved Web pages and for the times between retrievals. By picking distributions with infinite variance, our model accounts for traffic with long range dependence since it has been shown that on-off source models exhibit long range dependence if either the on or the off periods have infinite variance. The insensitivity property implies that when the means are specified these variances do not affect the steady-state probabilities.

The way in which feedback causes source rate reduction depends on the protocol. We provide models that are specific to TCP operating in conjunction with various cell or packet discard schemes. Feedback schemes other than TCP, such as ATM ABR, are similarly analyzable using our method provided the protocol specific efficiency-impairing effects are accounted for, and are left for future work.

We use the model to derive goodputs (information rate of successful transmissions divided by the speed of the access line). In the model, the goodput of a source inherits the insensitivity property. We compare the results of the model with measurements from detailed TCP simulations for TCP and TCP over ATM, with different buffer management schemes. The different buffer management schemes have different efficiency impairing effects. We use two distributions for files sizes and think times. Our traffic model agrees with measured traffic in the sense that comparisons of simulated TCP traffic, with Pareto think times, to measured Ethernet traffic show qualitatively similar autocorrelations. Also, the simulated and measured traffic have long range dependence although with different Hurst parameters.

Our key results, which are presented for the TCP protocol, are as follows: (1) The goodputs and the fraction of time that the system has some given number of transferring sources are insensitive to the distributions of transfer (file or page) sizes and think times except through the ratio of their means. Thus, apart from network round-trip times, only the ratio of average transfer sizes and think times of users need be known to size the network for achieving a specific quality of service. (2) The Engset model can be adapted to accurately compute goodputs for TCP and TCP over ATM, with different buffer management schemes. Though only these adaptations are given in the paper, the method based on the Engset model can be applied to analyze other feedback systems, such as ATM ABR, by finding a protocol specific adaptation. Hence, the method we develop is useful not only for analysing TCP using a source model significantly different from the commonly used persistent sources, but also can be useful for analysing other feedback schemes. (3) Comparisons of simulated TCP traffic to measured Ethernet traffic shows qualitatively similar second order autocorrelation when think times follow a Pareto distribution with infinite variance. Also, the simulated and measured traffic have long range dependence. In this sense our traffic model, which purports to be Web-user-like, also agrees with measured traffic.