Bottleneck structures have been recently introduced as an efficient mathematical framework for modeling communication systems. Leveraging fast computational graph algorithms from the field of automatic differentiation such as backpropagation, these structures can solve certain wired network problems two to three orders of magnitude faster than traditional network simulators, without losing significant precision. In this paper, we extend the theory of bottleneck structures to incorporate channel interference, enabling their application to wireless network modeling. This generalization leads to the development of a novel mathematical simulator for wireless networks. By introducing a new class of water-filling algorithms that exploit the structure of the computational graph, we demonstrate that bottleneck structures can simulate wireless networks with thousands of user equipments (UEs) in just a few seconds—achieving speedups of two to four orders of magnitude compared to state-of-the-art linear and non-linear programming solvers. For example, in a network with approximately 3000 UEs and 30 base stations, our approach reduces computation time from 145 to 1.08 seconds when assuming generalized processor sharing (GPS) schedulers, and from 2470 to 0.04 seconds when assuming proportional fair (PF) schedulers. To showcase the practical utility of this framework in network optimization, we also integrate bottleneck structures into a mixed-integer linear programming solver and apply it to the antenna placement problem, demonstrating scalability to networks with thousands of UEs.
