The study of round-trip time (RTT) measurements on the Internet is of particular importance for improving real-time applications, enforcing QoS with traffic engineering, or detecting unexpected network conditions. On large timescales, from 1 hour to several days, RTT measurements exhibit characteristic patterns due to inter and intra-AS routing changes and traffic engineering, in addition to link congestion. We propose the use of a nonparametric Bayesian method to fully estimate HMM parameters from delay observations, including the number of states. We validate the model through three applications: the clustering of RIPE Atlas measurements, the detection of significant delay changes, and the reduction of the monitoring cost in routing overlays using Markov decision processes.