Facility service balance problem with information feedback mechanism in the virtual–real interaction network

Considering the information interaction in the virtual–real network, this paper introduces a novel three-layer model that explores the integrated influence between virtual and real networks. Existing models often fail to capture the dynamic feedback between these networks and do not effectively simulate integrated decision-making processes. Focusing on the Facility Service Balance Problem, we aim to optimize resource allocation and information diffusion in response to real-world events like natural disasters or large-scale activities. Based on the Linear Threshold model, the Feedback Linear Threshold model, which incorporates feedback mechanisms between virtual and real networks and integrates both original and feedback information in the activation function of nodes, has been proposed to better simulate the information feedback and integrated decision-making process. Then, combined with location-based interpersonal and online social networks, a comprehensive framework that models decision-making processes without direct influence between decision-makers has been provided, focusing on the decision-making of individuals influenced by cumulative information, ultimately maximizing the facility service efficiency. Finally, conduct experiments have been conducted, using two types of data to test the general effectiveness of the feedback mechanism.