Revisiting the coupon collector’s problem to unveil users’ online sessions in networked systems

Accuratecomprehension of users’ behavior is paramount for understanding the dynamics of several systems, such as e-commerce platforms, social networks, and mobile computing. To this end, several strategies have been proposed to obtain data sets based on the capture of usage information, which can then serve for user analytics. A popular strategy consists of taking periodic snapshots of online users, a practical instance of the coupon collector’s problem tailored to users monitoring in networked systems. Due to system-specific limitations, however, users may fail to appear in some snapshots, although online. To bridge this gap, we present a methodology to correct ill-collected snapshots and build more accurate data sets. In summary, we formally model user snapshotting as an instance of the coupon collector’s problem, estimate the probability that some users are missing in a given snapshot following a Bernoulli process, and correct those snapshots should the probability exceed a given threshold.