Telecommunications networks have migrated from circuit based telephony services to packet based broadband network services. Merging with computer networks, they are being integrated with non-real-time data services on classical Internet integrated multimedia services, including real time voice, video and services on the new generation Internet. Thus, the concepts and requirements of quality of service (QoS) and traffic modelling have also been changed significantly. However, real time services such as voice and video are inelastic, as the transmission bandwidth, transmission time and QoS requirements need to be kept within strict limits and hence are not flexible. On the other hand, elastic services such as file transfer and Web surf are much relaxed with QoS and network resource requirements. Networks need to meet the requirements of both types of services by providing different classes of network services, including best effort service at one end of the spectrum, guaranteed service on the other end, and some others in between, with controlled traffic load. Traffic modelling is one of the important aspects to be considered to meet QoS requirements of services and efficient utilisation of network resources. The paper discusses important QoS issues, techniques for measurement and analysing Internet traffic, and new trends and methodology for Internet traffic modelling. It also presents the results based on the measured Internet traffic to validate the new model and the potential of the model to capture the characteristics of traffic for the Internet.