Over the years researchers have used Weibull distribution to model packet level Internet traffic behaviour without any physical or analytical justification other than its parameter flexibility and heavy-tailed behaviour. In this article we present an extensive data analysis of two-way traffic in various Internet access and backbone core links and show analytically why Internet traffic converges to Weibull distribution as traffic moves from access to core links. In addition we show the flexibility of Weibull distribution in capturing stochastic properties of Internet traffic at packet, flow and session levels in various access and backbone core links. An extensive literature survey with new developments in Internet traffic count data modelling has been presented. The contributions in this article establish the notion of the “Renewal of Renewal Theory in Internet Traffic Modelling”. This is the first study which presents a duplex analysis of all structural components of Internet traffic (packets, flows and sessions) at access and backbone core tiers of Internet. The results has been validated by using real traffic data fitness tests and trace driven queueing performance evaluation. The results of this article will help researchers use simple renewal processes as a better alternate to complex self-similar or modulated stochastic processes for modelling all structural components of Internet traffic at any time scale with physical justifications.