{'fraction_non_alphanumeric': 0.022123893805309734, 'fraction_numerical': 0.0029498525073746312, 'mean_word_length': 5.112612612612613, '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}}
DeP-D: A Decentralized Primal-Dual Optimization Algorithm for Industrial Wireless Sensor Networks

Industrial Wireless Sensor Networks (IWSNs) are emerged as flexible and cost-efficient alternatives to the traditional wired networks in various monitoring and control applications within the industrial domain. Low delay is a key feature of delay-sensitive applications as the data is typically valid for a short interval of time. If data arrives too late it is of limited use which may lead to performance drops or even system outages which can create significant economical losses. In this paper, we propose a decentralized optimization algorithm to minimize the End-to-End (E2E) delay of multi-hop IWSNs. Firstly, we formulate the optimization problem by considering the objective function as the network delay where the constraint is the stability criteria based on the total arrival rate and the total service rate. The objective function is proved to be strictly convex for the entire network, then a Decentralized Primal-Dual (DeP-D) algorithm is proposed based on the sub-gradient method to solve the formulated optimization problem. The performance of the proposed DeP-D is evaluated through simulations and compared with WirelessHART network and the results show that the proposed DeP-D can achieve at least 40% reduction in the average E2E delay.