A packet switched network such as the Internet provides only the best-effort service for users. Recent studies of the characteristics of packet arrival on a packet switched network have shown a self-similar property with long-range dependence, and also show a heavy-tailed distribution. This paper investigates end-to-end performance of the Internet empirically. It focuses on the inter-arrival process of packets and the property of packet loss between end-to-end hosts. We show that both the inter-arrival process and loss events are self-similar with a long-range dependence property. The inter-arrival process of packets has a heavy-tailed distribution which sums up the difference of all queues in intermediate routers.