Spatial Network Calculus and Performance Guarantees in Wireless Networks

This work develops a novel approach towards performance guarantees for all links in arbitrarily large wireless networks. It introduces spatial regulation properties for stationary spatial point processes and develops 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 leads to upper bounds on the interference power; 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. Focusing on device-to-device networks, we then derive universal bounds on the SINR based on spatial regulations and, in turn, link service guarantees assuming information theoretic achievability. They are combined with classical network calculus to provide end-to-end latency guarantees for all packets in such wireless queuing networks. Such guarantees do not exist in networks that are not spatially regulated, e.g., Poisson networks.