{'fraction_non_alphanumeric': 0.010452961672473868, 'fraction_numerical': 0.0, 'mean_word_length': 5.764705882352941, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Basic theory and some applications of martingales

This tutorial surveys the fundamental results of the theory of martingales from the perspective of the performance engineer. We will present the fundamental results and illustrate their power through simple and elegant proofs of important and well-known results in performance analysis. The remainder of the tutorial will introduce the martingale functional central limit theorem and semi-martingale decomposition methodology for the characterization and proof of heavy-traffic limit results for Markovian queueing systems.