Modelo de mistura de processos pontuais estocásticos para tempos entre eventos de serviços na Web

Abstract

In the present work we propose a mixture of point processes models, distinct and stochastically independent, for Internet services inter-event times. One is the Self-Feeding Process (SFP) and the other is the homogeneous Poisson process (PP). The SFP model is an excellent descriptor for Web random event times. The motivation for the use of the PP is the empirical verification that the long periods of inactivity predicted by the SFP do not occur in some instances. To disentagle the two processes, we use the EM algorithm. In the E step we approximate the maximum of the likelihood function by its expected value because the events labels are not known. A hypothesis test was applied to check either the additional free variable in the mixture model is actually needed or a single pure process, SFP or PP, is sufficient to describe the observed stochastic process. The results were satisfactory since the topics are well fitted by the proposed model for nine real data sets. In addition, two applications were proposed: anomaly detection and bursts detection.