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Efficient communication in Bluetooth networks requires design of intra and inter-piconet scheduling algorithms, and therefore numerous algorithms have been proposed. However, due to complexities of the Bluetooth MAC, the performance of these algorithms has been analyzed mostly via simulation. We present exact analytic results regarding the exhaustive, gated, and limited (pure round robin) scheduling algorithms in piconets with unidirectional traffic. We show that, surprisingly, in symmetrical piconets with only uplink traffic, the mean waiting time is the same for the exhaustive and limited algorithms. This observation is extended for time-division-duplex systems with arbitrary packet lengths. Furthermore, we show that the mean waiting time in a piconet with only uplink traffic is significantly higher than its corresponding value in a piconet with only downlink traffic. We then demonstrate the difficulties in analyzing the performance of the exhaustive and gated algorithms in a piconet with bi-directional traffic. Finally, we numerically compare the exact results to approximate results, presented in the past.