Delay Distributions on Fixed Internet Paths

–Based on end-to-end delay measurements of IP probe-packets over a Þxed path obtained from RIPE NCC, we model the stochastic part of the delay and propose statistical methods to analyse the data. The Internet traffic on the Þxed path interferes with the IP probe-packets. This is modeled as an alternating on/off renewal process. On top of the delay caused by Internet traffic, the IP probe-packets experience a random processing delay due to scheduling and conversing of IP packets to various lower layer technologies in the routers on the Þxed path. The total delay is both modeled parametricly and by a non-parametric method. Although the data indicates that the end-to-end delay distribution is heavy tailed, neither a Pareto nor Weibull law provided sufficient accurate Þts. The non-parametric method essentially enabled a stable deconvolution that led to the delay due to Internet traffic. Furthermore, the non-parametric method provides good estimates of the probability that the path is not loaded and bounds on the queueing tail probabilities. Especially these qualiÞers are useful for deploying real-time services on Internet. Keywords–End-to-end delay, stochastic modeling.