Game workloads exhibit predictable daily and weekly changes

8: FFT of the player load from four games over one year.

9: Week-to-week PDF of percent load changes for the top 5 games of 2004

(a) Instantaneous	(b) Mean	(c) Maximum

10: Population trends for Half-life and other games with an averaging window of one week

(a) Half-Life	(b) Other games

Intuitively, it is reasonable to assume that usage is strongly tied to the daily and weekly activities of players. Figure 7 shows the global player population of four consecutive weeks starting from 3/1/2003 for three popular games: America's Army, Half-Life, and Neverwinter Nights. As expected, the figure shows that the workload has regular daily cycles and that over this one month period the workload does not vary significantly from week-to-week. In fact, for all three games, the trends as well as the maximum and minimum points match up at identical points in time during the week. We observe similar results over other parts of the year with the only anomalies caused by service outages and by holidays. To further demonstrate the cyclical nature of gaming workloads, we take one year's worth of game server load samples across a variety of games and plot the Fast Fourier Transform (FFT) of the data. The FFTs have been scaled so that they can be plotted together. As Figure 8 shows, the FFT contains strong peaks at the 24-hour cycle for each of the games. There is also a significant peak at the 168-hour (one week) cycle for two of the games as well. This corresponds to an increase in player usage on the weekends during some parts of the year. Papagiannaki et. al use wavelet multiresolution analysis (MRA) on another long-term data series [26], and model their series as a 12-hour and 24-hour cycle plus a trend. We were unable to apply this technique however, due to the reliance of wavelet MRA on resolutions that are factors of two apart. The difference between our two cycles is seven.

In order to quantify the week-to-week variation of game workloads, Figure 9 shows distribution of week-to-week load changes of the top 5 games during 2004: Half-Life, Battlefield 1942, Medal of Honor: Allied Assault, America's Army, and Neverwinter Nights. Figure 9(a) plots the distribution of instantaneous load changes between identical points in time of consecutive weeks, while Figure 9(b) plots the change in average daily load between the same day of the week of consecutive weeks. Finally, Figure 9(c) plots changes in maximum daily load between the same day of the week of consecutive weeks. The figures fit a `t' location-scale distribution, which has three parameters, a scale parameter $\sigma>0$, a location parameter $\mu$, and a shape parameter $\nu>0$. The density function for this distribution is as follows:

$f(x) = \frac{\Gamma( \frac{\nu +1}{2})}{ \sigma \sqrt{\nu \pi} \Gamma(\frac{\nu}{2})} ( \frac{\nu + (\frac{x-\mu}{\sigma})^2}{\nu})^{-\frac{v+1}{2}}$

Note that if $x$ is `t' location-scale distributed, $\frac{x-\mu}{\sigma}$ is Student's `t' distributed with $\nu$ degrees of freedom. As illustrated in Figure 9, we find a very good fit for all the three plots. Based on this observation, we draw two main conclusions with regard to resource usage:

• As the figures show, almost all week-to-week load variations are under 10% of the previous week's workload. Such behavior makes it relatively easy for game and infrastructure providers to provision and predict resource usage on a weekly basis.

• The above distribution fitting of load variations indicates that it is feasible to model the week-to-week load variations using such standard distributions. We are exploring the feasibility of online parameter estimations for using this model in resource provisioning.