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Measurements on a high-performance Ethernet are shown to match well a truncated Cauchy probability distribution, with a much better fit over smaller file/request sizes than the commonly used Pareto distribution. We observe self-similar characteristics in the traffic at both file servers and at a CPU server elsewhere in the network, which targets, predominantly, file and web servers. This suggests propagation of self-similarity. A simulation model of a single server with Poisson arrivals and Cauchy service demands yields a departure process that follows a power law and matches closely the observed traffic. The simulation is also used to investigate the link between the power laws in the request size distribution and the network traffic by using Lévy distributions for the request sizes. This suggests a link between file/request size distribution and self-similarity in traffic, leading to the possibility of using conventional queueing network performance models with processor sharing queueing discipline. This idea is further supported by an additional simulation experiment and suitable models are proposed.