Modeling Email Server I/O Events As Multi-temporal Point Processes

Abstract

We model the read-workload experienced by an email server as a superposition of reads performed by different software clients at non-deterministic times, each modeled as a dependent point process. The probability of a read event occurring on an email is affected, among others, by the age of an email and the time of the email recipient’s day. Unlike the more commonly encountered variants of point processes – the one-dimensional temporal, or the multi-dimensional spatial or spatio-temporal – the dependence between the different temporal axes, age and time of day, is incorporated by a point process defined over a non-Euclidean manifold. The used model captures the diverse patterns exhibited by the different clients, for example, the influence of age of an email, time of the user’s day, recent reads by the same or different clients, whether the client is controlled directly by the user, or is a software-agent acting semi-autonomously on the user’s behalf or is a server-side batch job that attempts to avoid adverse impact on user’s latency experience. We show how estimating this point process can be mapped to a Poisson regression, thereby saving the time to implement custom model training software.