Probability Models for the Splitting Discovery Algorithm in Wireless Networks

In this letter, we propose probability models and derive novel analytical results for the splitting discovery algorithm, which could be applied to medium access control and leader selection in wireless networks. When the splitting discovery algorithm is applied to wireless medium access control, we derive the expected value and the probability distribution function for the number of steps it takes to discover the node with the largest instantaneous channel gain. In addition, we derive the corresponding network throughput. We show that our equation-based numerical results are consistent with event-based simulation results.