{'fraction_non_alphanumeric': 0.021611001964636542, 'fraction_numerical': 0.005893909626719057, 'mean_word_length': 5.175757575757576, '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}}
Multiscale Queuing Analysis August 31 , 2004

We develop a new approach to queuing analysis for an infinite-length queue with constant service rate fed by any traffic process. Our approach provides important theoretical results, is easy to implement in practice, and is particularly relevant to queues fed with long-range-dependent (LRD) traffic. We use traffic statistics at only a small fixed set of time scales and develop three approximations for the tail queue probability. These are non-asymptotic, that is they apply to any finite queue threshold. Simulations with LRD traffic models and Internet traces demonstrate their accuracy. Besides non-asymptotic error bounds, asymptotic decay rates, and error bounds for the approximations, we prove an optimality property of exponential time scales. Simulations reveal that the second-order correlation structure of traffic by itself does not determine queuing behavior and that the tails of traffic marginals at different time scales have a strong impact on queuing.