Bluetooth suits for diverse computing and communication devices and becomes a built-in feature in millions of products. One of important problems for Bluetooth nodes is to become aware of their neighbors. Since the process is time consuming it is critical to compute the neighbor discovery timeouts. Therefore the mean and variance of the device discovery time is analyzed considering different magnitude of error. Based on the results, the discovery timeout and state residence interval in the light of the error in Bluetooth network is computed. The simulation results show that the connection establishment delay in the algorithm is flexible by adjusting the parameters proposed in this paper.