This paper presents the characteristics and modeling of VoIP traffic for a real network. The new model, based on measured data, shows a significant difference from the previously proposed models in terms of parameters and their effects. It is found that the effects of background noise and ringing tones have essential influences on the model. The observed distributions of talkspurt and silent durations have long-tail characteristics and considerably differ from the existing models. An additional state called "Long burst", which represents the background noise at the talker's place, is added into the continuous-time Markov process model. The other three states, "Talk", "Short silence" and "Long silence", represent the normal behavior of the VoIP user. Models for conversational speech containing the communication during the dialogue are presented. In the case of the VoIP traffic aggregation, the simplified models, which neglect the conversation's interaction, are proposed. Depending on the occurrences of background noise during the speech, the model is classified as "noisy speech" or "noiseless speech". The measured data shows that the background noise typically increases the data rate by 60%. Simulation results of aggregated VoIP traffic indicate the self-similarity, which is analogous to the measured data. Results from the measurements support the fact that except the ringing duration the conversations from both the directions can be modeled in identical manner.