Probabilistic sampling of finite renewal processes

TL;DR

This paper develops a statistical framework for inferring the original distributions of finite renewal processes from sampled data, motivated by Internet traffic measurement challenges.

Contribution

It introduces a novel method for estimating distributions of total renewals and interrenewal times from sampled finite renewal processes.

Findings

Effective inference of original distributions from sampled data

Applicable to Internet traffic flow analysis

Addresses challenges of limited storage and processing capacities

Abstract

Consider a finite renewal process in the sense that interrenewal times are positive i.i.d. variables and the total number of renewals is a random variable, independent of interrenewal times. A finite point process can be obtained by probabilistic sampling of the finite renewal process, where each renewal is sampled with a fixed probability and independently of other renewals. The problem addressed in this work concerns statistical inference of the original distributions of the total number of renewals and interrenewal times from a sample of i.i.d. finite point processes obtained by sampling finite renewal processes. This problem is motivated by traffic measurements in the Internet in order to characterize flows of packets (which can be seen as finite renewal processes) and where the use of packet sampling is becoming prevalent due to increasing link speeds and limited storage and processing capacities.