The performance of a single Bluetooth piconet is analyzed using the theory of M/G/1 queues with vacations. Analytical results for probability distributions of packet access time and service cycle time are derived. Two scheduling policies are modeled and compared: exhaustive service was found to perform better, but limited service does not incur the risk of starvation. A hybrid scheme known as k-limited scheduling is shown to provide a reasonable tradeoff between performance and fairness. Results were confirmed through simulations.