Analytical Evaluation of PHM Convergence

The parallel hierarchical matching (PHM) algorithm is a distributed maximal size matching scheduler for virtual output-queued switches. In a previous letter, we formulated an upper bound on the maximum number of iterations PHM requires to achieve a maximal size matching in any traffic scenario. In this letter, we follow an analytical approach to find the average number of iterations for PHM to achieve a maximal size matching under diverse traffic models. The estimated number of iterations is$O(log_2N)$, as in the case of iSLIP-like algorithms.