Analytic model for the Event Filter top-of-rack switch buffer occupancy in the HL-LHC ATLAS Data Acquisition system

In this document we derive the analytic formula that estimates the maximum buffer occupancy in the Event Filter top-of-rack switch when performing full Event Building in the ATLAS Data Acquisition system. This work has been developed in the context of the ATLAS DAQ Network upgrade project for the High-Luminosity LHC, with the aim of assisting the network design and provide a qualitative model of the buffer of the top-of-rack switches to be deployed in the Event Filter farm. The modeling of the network traffic and switch buffering profiles has been highly simplified. The assumptions and simplifications taken, as well as the validity of the results are duly justified. Despite the naive approach to the problem under study, the results obtained with the formula have been confronted against the measurements taken in a test-bench, proving that the formula predicts correctly the shape of the laws governing the buffer occupancy