{'fraction_non_alphanumeric': 0.015748031496062992, 'fraction_numerical': 0.0, 'mean_word_length': 5.878378378378378, '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}}
APPROXIMATING QUEUES IN SLOWLY VARYING STATIONARY ENVIRONMENTS

We provide linear approximations to the marginal distributions for a class of infinite-state continuous-time stationary Markov chains in slowly varying environents. We take an approach motivated by light-traffic approximations to stationary point processes, which permits us to consider general stationary environments. Under mild assumptions we show that Jackson networks with routing not affected by the environment, belong to this framework.