Weibull mixture model to characterise end-to-end Internet delay at coarse time-scales

Traces collected at monitored points around the Internet contain representative performance information about the paths their probes traverse. Basic measurement attributes, such as delay and loss, are easy to collect and provide a means to both build and validate empirical performance models. However, the task of analysis and extracting performance conclusions from measurements remains challenging. Ideally, performance modelling aims to find a set of self-contained parameters to describe, summarise, profile and easy display network performance status at a time. This can result in the provision of meaningful information to address applications in fault and performance management, hence providing input to network provisioning, traffic engineering and performance prediction. In this work we present the Weibull Mixture Model, a method to characterise endto- end network delay measurements within a few simple, accurate, representative and handleable parameters using a finite combination of Weibull distributions, with all the aforementioned benefits. The model parameters are related tomeaningful delay characteristics, such as average peak and tail behaviour in a daily profile, and can be optimally found using an iterative algorithm known as Expectation Maximisation. Studies on such parameter evolution can reflect current workload status and all possible network events impacting packet dynamics, with further applications in network management. In addition, a self-sufficient procedure to implement the Weibull Mixture Model is presented, along with a set of matching examples to real GPS synchronised measurements taken across the Internet, donated by RIPE NCC.