Round-Trip Times are one of the most commonly collected performance metrics in computer networks. Measurement platforms such as RIPE Atlas provide researchers and network operators with an unprecedented amount of historical Internet delay measurements. It would be very useful to process these measurements automatically (statistical characterization of path performance, change detection, recognition of recurring patterns, etc.). Humans are quite good at finding patterns in network measurements, but it can be difficult to automate this and enable many time series to be processed at the same time. In this article we introduce a new model, the HDP-HMM or infinite hidden Markov model, whose performance in trace segmentation is very close to human cognition. We demonstrate, on a labeled dataset and on RIPE Atlas and CAIDA MANIC data, that this model represents measured RTT time series much more accurately than classical mixture or hidden Markov models. This method is implemented in RIPE Atlas and we introduce the publicly accessible Web API. An interactive notebook for exploring the API is available on GitHub.