Modeling large-scale live video streaming client behavior

Abstract

The live streaming of large-scale events over the Internet attracts a highly diverse audience. Despite the progress in streaming technologies, which employ adaptive bitrate to dynamically adjust the streaming of individual clients to reflect their resource availability, content providers still struggle to efficiently match provisioned capacity and demand in such events. In this paper, we present an in-depth characterization and modeling of client behavior during the live streaming of the 2018 FIFA World Soccer Cup. We analyze logs covering more than 60 million streaming sessions collected from servers of one of the major content providers in Latin America. We characterize key features of the workload, such as the number and duration of sessions as well as transmission quality (i.e., bitrate), shedding new light on the workload of a major content provider during a unique large-scale streaming event. We then propose a simple hierarchical model to describe the typical behavior of individual clients both at the session and video bitrate adaptation layers. Taking a step further, we employ non-supervised clustering to identify classes of client behavior and generate specialized models, one for each class. Our evaluation shows that the specialized models are more accurate compared to the single general model, as it can better describe the diversity of client behavior patterns.

Appendix: Best fitted distributions

Table 2 presents the fitting parameters of our behavior model. The clustering process originates seven client clusters. As we can see, these groups have different regimes, that are reflected on the variability of the fitted distributions.

The PMF of the Negative Binomial is $p(k,n,p) = \left( {\begin{array}{c}k+n-1\\ n-1\end{array}}\right) p^n(1-p)^k$ for $k \ge 0$. The PDF for Exponentiated Weibul is $f(x,a,c) = ac(1-\mathrm{exp}(-x^c))^{a-1}\mathrm{exp}(-x^c)x^{c-1}$ with $x>0,a>0,c>0$ and a and c as shape parameters. The PDF of Power log-normal is $f(x,c,s) = \frac{x}{cs}\phi (log(x)/s)\varPhi (-log(x)/s))^{c-1}$ for $x \ge 0$ and $a > 0$. The $\phi$ is the normal PDF, $\varPhi$ is is the normal cdf, and $x> 0, s, c > 0$. c and s are the shape parameter. The PDF for Log-normal distribution is $f(x,s) = \frac{1}{sx\sqrt{2\pi }}e^{(-1/2(\frac{log(x)}{s})^2)}$ with $x,s > 0$ and s as shape parameter. The PDF of Gamma distribution is $f(x,a) = \frac{x^{a-1}\mathrm{exp}(-x)}{\varGamma (a)}$ for $x \ge 0$ and $a > 0$. The $\varGamma (a)$ is the gamma function and a is the shape parameter. The Erlang distribution is a special case of the Gamma distribution, with the shape parameter a as an integer. The PDF for Generalized Gamma distribution is $f(x,a,c) = \frac{|c|x^{ca-1}\mathrm{exp}(-x^c)}{\varGamma (a)}$ with $x \ge 0$, $a > 0$ and $c \ne 0$. a and c are the shape parameters and $\varGamma (a)$ is the gamma function. The PDF for Weibull (a.k.a. Frechet right) is $f(x,c) = cx^{c-1}\mathrm{exp}(-x^c)$ for $x>0$ and $c>0$ and c as shape parameter. The PDF for Exponential Power distribution is $f(x,b) = bx^{b-1}\mathrm{exp}(1+x^{b}-\mathrm{exp}(x^{b}))$ with $x \ge 0$ and $b > 0$ as shape parameter. The PDF for Beta distribution is $f(x,a,b) = \frac{\varGamma (a+b)x^{a-1}(1-x)^{b-1}}{\varGamma (a)\varGamma (b)}$ for $0 \le x \le 1, a> 0, b > 0$ where $\varGamma$ is gamma function.

Table 2 Fitted parameters for the groups of clients (top) and for the complete dataset (bottom)