Definition: Finite periodic transport model

Let $Q$ be a finite strongly connected directed quotient graph. Vertices include register type and schedule phase. Every edge $e$ has a displacement ${\Delta }_e\in {\mathbb{R}}^D$ and duration $u_e\ge u_{\min }>0$. Its periodic lift permits translated copies of the transitions. Waiting without displacement is allowed.

For a simple directed cycle $c$, set

Define