{'fraction_non_alphanumeric': 0.031484257871064465, 'fraction_numerical': 0.008995502248875561, 'mean_word_length': 4.475409836065574, '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}}
The Correlation Coefficients of the Queue Lengths of Some Stationary Single Server Queues

Until recently there has been little systematic work on the second-order properties of queueing processes. The aim of this paper is to study systematically the second-order properties of the queue length processes embedded at departure epochs in the M/G/1 and bulk service M/G/1 queues, and at arrival epochs in the GI/M/1 queue. In the latter case our results extend those of Daley [7], while in the ordinary M/G/1 queue our work parallels Daley's [6] discussion of waiting times in the same system. In the final section we briefly discuss two discrete time queueing systems.