This paper examines the performance of a new Hidden Markov Model (HMM) structure used as the core of an Internet traffic classsifier and compares the results against other models present in the literature. Traffic modeling and classification find importance in many areas such as bandwidth management, traffic analysis, prediction and engineering, network planning, Quality of Service provisioning and anomalous traffic detection. The new HMM structure, which takes into account the packet payload size (PS) and the inter-packet times (IPT) sequences, is obtained by concatenation of a first part which is framed with a HMM profile with another part whose structure is that of a fully-connected HMM. The first part captures the specific properties of the initial protocol packets while the second part captures the statistical properties of the whole sequence present in the flow. Models generated are found to increase the accurate in classifying different traffic classes in the analysed dataset. The average accuracy obtained by the classifier is 62.5% having seen only five packets, 80.0% after examining 13 packets and 95.5% after seeing the unidirectional entire flow.