The real-time and reliable transmission of data packets is a critical foundation for ensuring Internet of Things applications. Therefore, how to ensure the timely reliability of wireless sensor networks has become a hotspot. However, existing timely reliability models often overlook the impacts of energy depletion and channel capacity randomness on wireless transmission. Additionally, most evaluations focus on single-hop, single-path scenarios, while practical data transmission typically requires multi-hop and multi-path strategies. To overcome the above shortcomings, this study conducts the timely reliability evaluation and optimization of wireless sensor networks considering channel capacity randomness and energy depletion. First, focusing on data transmission delay modeling, this study emphasizes the effects of energy depletion and channel capacity randomness on wireless data transmission, and further proposes a timely reliability evaluation model based on the G/G/1 queuing model. Secondly, to tackle the computational challenges of multi-hop and multi-path data transmission, this study proposes a timely reliability solving algorithm that integrates the binary decision diagrams with Monte Carlo simulation.. Building on these foundations, this study develops a periodic optimization model for signal transmission power, balancing sensor lifetime and network transmission performance. Finally, taking the military Internet as an example, the effectiveness of the proposed method is verified.

Satellite-terrestrial networks (STNs) are a promising paradigm for providing Internet services for users globally. Since the dynamics of service resources and the uncertainty of computational requests, how the service resources in STNs can be efficiently exploited to execute differentiated computational tasks is an essential challenge. In this work, we investigate the dynamic task scheduling in the integrated cloud-edge STNs. First, we propose a cloud-edge collaborative computing framework in STNs, where the computational tasks of users can be processed collaboratively by satellite edge servers, terrestrial edge servers, and cloud servers. Based on this framework, a dynamic task scheduling problem is formulated with the objective of maximizing the task success rate. Second, to make effective real-time decisions at decision points in the dynamic scheduling process, we develop a scheduling heuristic with the routing rule and queuing rule, which incorporates dynamic features related to servers, computational tasks, and network environments. Third, to automatically learn the scheduling heuristic, we propose a multitree genetic programming with rule reconstruction (MTGPRR), which introduces a selective reconstruction operator. This operator increases the chance of matching good rules with other rules by recombining common individuals and elites. Experimental results demonstrate that the proposed MTGPRR performs significantly better than the state-of-the-art methods in improving the task success rate. Moreover, the evolved scheduling heuristic has good interpretability, which is important for practical applications.