Load distribution of different users

On average, we observed that a user receives 2.3 notification messages containing a total of 0.2 KBytes per day, and 16.1 notification messages containing 1.4 KBytes of data per week. There is a significant variation in the clients' usage -- during the week that we studied, some clients received over 1000 messages (containing as high as 0.1 MB of data), while other clients received fewer than 10 messages containing as little as a few hundred bytes of data. Figures 8 and 9 show the total number of messages and the total number of bytes received by different users on a log-log scale, respectively. Both curves fit very well with a straight line (i.e., follow Zipf-like distribution), except at the tail where there is a sudden drop. We compute the values of $\alpha$ using least-square fitting, after excluding the sharp drop at the tail. The value of $\alpha$ is 0.4437 when usage is defined as the number of messages; when usage is defined as the number of bytes, its value is 0.4567.

  

Figure 8: The total number of notification messages received by different users.

  

Figure 9: The total number of notification bytes received by different users.

To further study how usage is distributed across different clients, we plot the cumulative distribution of client usage in Figure 10. As the figure shows, the top 5% of the clients received 28% of the notification messages, and 25% of the notification bytes; the top 10% of the clients received 40% of the notification messages, and 38% of the notification bytes. It is clear that a small fraction of users consume a significant fraction of the system and network resources. It is also interesting to note that the CDF curves are similar for the two different ways of defining usage. The similarity of the curves shows that each user receives a similar number of bytes per message.

  

Figure 10: Cumulative distribution of different clients' usage.

  

Figure 11: Number of bytes and messages served by the notification servers during the days in the week.

The cumulative load imposed by all users (in terms of number of messages and the number of bytes sent by the servers) is shown in Figure 11. The figure shows that the number of messages and the number of bytes are fairly constant during weekdays but exceed the number sent during the weekend. This confirms what one would expect, i.e., information alerts are more frequently generated when people are working.