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In this paper, we aim at the point which the sensing coverage for target monitor tracking and the connectivity coverage for information transmitting of WSN claim to robust, anti-fragility. We firstly present and prove a profound sensing radius of nodes; this radius can make each objective point of monitor area fall under the sensing range of at least one sensor node by the probability of tending to 1 at any time. Secondly, we analyze the problem of connectivity coverage of WSN, also present and prove a probability inequality of active nodes, which can be of the judgment scale and the critical threshold that the connectivity of WSN not to be destroyed. Thirdly, under the premise which the necessity of connectivity of WSN is satisfied, we present an algorithm that provided with robust connectivity of big probability, and doing the simulation analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate throughput capacity theories of Hierarchical Wireless Sensor Networks (H-WSN). Firstly, we introduce the structural protocol model, node mobility tracking model and conflict graph model of H-WSN. Secondly, we give some fundamental definitions about conflict graph and conflict event. Thirdly, a fundamental theorem about graph theory is given, and then the throughput capacity is turned to the problem that can be translated into linear constraints system, and can be gotten by finding the feasible solution of linear system. Finally, we propose and prove a critical inequality of throughput capacity of H-WSN. We also propose and prove a gradual probabilistic quality and the specific expression of expectant availability of throughput capacity of H-WSN. The results enrich the theory of some famous conclusions about throughput capacity and the information theory of wireless networks. [ABSTRACT FROM AUTHOR]