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This paper discusses self-similarity in the uplink traffic of CDMA cellular packet communications. We estimate the Hurst parameter of transmission delay time, which is collected by using computer simulation, and analyze its power spectrum. We find that self-similarity and the 1/f power spectrum are observed in transmission delay time on the uplink of a CDMA cellular packet system. Self-similarity is also analyzed for various errors of transmission power control in order to discover the system conditions under which self-similarity appears. The results of these analyses show that the power control error has a large effect on the self-similarity: self-similarity appears in a system with an accurate power control, whereas it does not appear in a system with a large power control error.