Generating Function For Network Delay

TL;DR

This paper investigates the statistical distribution of network packet delays, demonstrating that exponential distribution accurately models delays in global networks, supported by precise experimental data and explicit mathematical functions.

Contribution

It provides an explicit form of the cumulative distribution and generating functions for network delays, along with an algorithm for estimating distribution parameters.

Findings

Exponential distribution best fits network delay data

Distribution parameters remain stable over 500-second intervals

Precise microsecond-level delay measurements support the analysis

Abstract

In this paper correspondence between experimental data for packet delay and two theoretical types of distribution is investigated. Statistical tests have shown that only exponential distribution can be used for the description of packet delays in global network. Precision experimental data to within microseconds are gathered by means of the RIPE Test Box. Statistical verification of hypothesis has shown that distribution parameters remain constants during 500 second intervals at least. In paper cumulative distribution function and generating function for packet delay in network are in an explicit form written down, the algorithm of search of parameters of distribution is resulted.