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The scale-invariant burstiness or self-similarity has been found in real network. Relation between self-similarity and network parameter is mainly discussed in the context of application layer, and this self-similarity is caused by the file size of Web servers or the duration of user sessions. Traffic dynamics, however, are mainly generated by physical conditions such as the resource restrainment, and the queue size on intermediate routers. In this paper, we have investigated queueing property for self-similar traffic using network simulator. After analyzing the simulated results, following properties were extracted. Firstly, the traffics with self- similar property are transmitted without consuming the queue resources on the bottleneck link. Secondly, queueing dynamics tend to exceed the linear manner for increase of packet flows.