{'fraction_non_alphanumeric': 0.02583276682528892, 'fraction_numerical': 0.0, 'mean_word_length': 5.976303317535545, '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}}
Reliability Calculus: A Theoretical Framework to Analyze Communication Reliability

Communication reliability is one of the most important concerns and fundamental issues in network systems, such as cyber-physical systems, where network components, sensors, actuators, controllers are interconnected with each other. These systems are prevalent in many safety-critical areas, including aerospace, automotive, civil infrastructure, energy, healthcare, manufacturing, and transportation, etc. In such systems, a single link failure, or communication delay could lead to catastrophic consequences. Hence, there is an urgent demand on efficient methodologies to model and analyze the delay distribution of control messages or feedback signals, especially when networks grow more complex and more heterogenous. In this paper, a calculus based on frequency domain analysis is developed to address this goal, so we can model and analyze the reliability of communication in large-scale compositional networked systems. Several network structures (e.g. serial, parallel, circular and backup) are defined as building blocks to model a wide variety of connections in networked systems. The advantages of the proposed theoretical framework over the traditional time domain approaches include the capability to capture higher order moments of system characteristics, calability to analyze the reliability of complex systems, efficiency in calculation and practicability in simulation.