On the Reproducibility of Daily Access Patterns in Public Online Services: a Two-compound Modelling Approach

Access dynamics in modern public online services is largely governed by erratic human behavior and complex user interactions typically exhibiting long-term memory. In most cases, the access patterns are non-stationary that requires relevant modeling approaches such as fractional Brownian motion, while the majority of conventional queuing theory models assume stationary arrivals. Here we suggest a simple two-compound model consisting of a regular trend and a stationary fractional gamma-distributed noise component as a replacement of an altogether non-stationary access pattern model. For selected examples of public online services we studied the reproducibility of the regular daily access patterns and the fluctuation component characteristics. We show explicitly that the combined model in most cases can be described by a few parameters that could be easily estimated from empirical observations that also appear largely universal for a particular service, thus allowing for conventional queuing theory based estimates with analytically achievable corrections.