This work develops a novel approach toward performance guarantees for all links in arbitrarily large wireless networks. It introduces a spatial network calculus, consisting of spatial regulation properties for stationary point processes and the first steps of a calculus for this regulation, which can be seen as an extension to space of the classical network calculus. Specifically, two classes of regulations are defined: one includes ball regulation and shot-noise regulation, which are shown to be equivalent and upper constraint interference; the other one includes void regulation, which lower constraints the signal power. These regulations are defined both in the strong and weak sense: the former requires the regulations to hold everywhere in space, whereas the latter only requires the regulations to hold as observed by a jointly stationary point process. Using this approach, we derive performance guarantees in device-to-device, ad hoc, and cellular networks under proper regulations. We give universal bounds on the SINR for all links, which gives link service guarantees based on information-theoretic achievability. They are combined with classical network calculus to provide end-to-end latency guarantees for all packets in wireless queuing networks. Such guarantees do not exist in networks that are not spatially regulated, e.g., Poisson networks.

翻译：本文针对任意大规模无线网络中所有链路的性能保证提出了一种新颖方法。该方法引入空间网络演算，包含对平稳点过程的空间调控性质及该调控的演算初步步骤，可视为经典网络演算在空间维度的扩展。具体定义了两种调控类别：一类包含球调控与散弹噪声调控（两者被证明等价并构成干扰上约束），另一类包含空洞调控（构成信号功率下约束）。这些调控分别以强、弱两种形式定义：前者要求调控在空间各处成立，后者仅要求调控在联合平稳点过程观测下成立。基于该方法，我们在合理调控下推导了设备到设备网络、自组织网络及蜂窝网络的性能保证。给出了所有链路信干比的通用上界，该上界基于信息论可达性提供链路服务保证。通过与经典网络演算相结合，实现了无线排队网络中所有数据包的端到端时延保证。此类保证在未实施空间调控的网络（如泊松网络）中并不存在。