{'fraction_non_alphanumeric': 0.016666666666666666, 'fraction_numerical': 0.0030303030303030303, 'mean_word_length': 4.798245614035087, '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 Markov Chain Description of A Workstation with Infinite Capacity

We present a discrete-time model for a workstation with infinite operating capacity at which one job arrives at every time instant and starts being processed. The jobs stay in the system for a possibly truncated geometrically distributed time period. We introduce and analyze a Markov chain which gives at any time a complete description of the state of the work on all jobs. Its positively recurrent states are the dyadic numbers in (0, 1]; we give its stationary distribution explicitly. For the busy period analysis of the workstation we study first-entrance problems of this Markov chain.