The statistical properties of traffic in Internet access networks have long been of interest to networking researchers and practitioners. In this paper, we analyse network traffic originating and terminating from various types of Internet access networks (Ethernet, Digital Subscriber Line, Wireless hotspot and their next tier Internet Service Provider's core network) and show that renewal processes having heavy-tail distributed interarrival times (also known as fractal renewal processes) have a great potential in capturing statistical properties of traffic in access networks.