{'fraction_non_alphanumeric': 0.008225616921269096, 'fraction_numerical': 0.0, 'mean_word_length': 5.454545454545454, '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}}
Global stability conditions for rate control with arbitrary communication delays

We analyze Kelly's optimization framework for a rate allocation problem in communication networks and provide stability conditions with arbitrary fixed communication delays. We demonstrate the existence of a fundamental tradeoff between users' price elasticity of demand and the responsiveness of resource through a choice of price function. We also show that the stability of the system can be studied by looking at a much simpler discrete time system that emerges from the underlying market structure of the rate control system with a homogeneous delay. We study the effects of nonresponsive traffic on system stability and show that the presence of nonresponsive traffic enhances the stability of system. We also investigate the system behavior beyond stable regime.