Spatial network calculus and performance guarantees in wireless networks

Network calculus is initially a methodology allowing one to provide

 performance guarantees in queuing networks subject to random arrival and

 service processes. It relies on the notions of regulated traffic arrivals

 and service curves or guarantees. It is a key design tool for

 latency-critical wireline communication networks where it allows one to

 e.g. guarantee bounds on the end-to-end latency of all transmitted

 packets. In wireless networks, service guarantees are more intricate as

 electromagnetic signals propagate in a heterogeneous medium where they

 are subject to unpredictable reflections and obstructions and as it is

 more difficult to isolate these signals from each other than in the

 wireline case. There is hence no methodology yet allowing one to give

 performance bounds holding for all links in wireless networks.

 In this talk, we present a novel approach toward such bounds for all

 links in arbitrarily large wireless networks. We introduce spatial

 regulation properties for stationary spatial point processes, which model

 transmitter and receiver locations, and develop the first steps of a

 calculus for this type of regulation.   Using this approach, we derive performance guarantees for

 various types of device-to-device and cellular wireless networks. Such guarantees do not exist in

 networks without spatial regulation, e.g., Poisson networks.