Spatial and Network Effects in Distributed System Design*

Designing a modern complex system requires keeping track of the interplay of the system's logical topology, spatial arrangement, and functionality. Existing frameworks mostly focus on how one of these aspects influences others in a single direction, rather than keeping track of the mutually deterministic nature of design elements. We demonstrate how to determine mutual influences of topology and spatial constraints on each other for a whole ensemble of possible system arrangements. We cast this problem in the modern graphical language of tensor networks, which facilitates computation and allows for extracting a variety of ensemble observables. We demonstrate the power of the approach on a model system routing problem from Naval Engineering, however the method is easily generalizable to other problems.