{'fraction_non_alphanumeric': 0.013089005235602094, 'fraction_numerical': 0.0013089005235602095, 'mean_word_length': 5.322314049586777, '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}}
A rational approximation approach to rare event probability estimation for high-performance systems

We derive first and second derivative estimators of the buffer overflow probability (defined as the probability that the queue length at steady state exceeds an integer value k) with respect to a service process parameter in a GI/G/1 queueing system using perturbation analysis techniques, The derivative estimates are obtained from a single sample path (simulation) generated at a parameter value where buffer overflow events are not rare and used to construct the response surface over a region where these events are relatively rare. We show that this response surface can be used to estimate rare event probabilities over certain parameter ranges of interest.