= Rearrangeable triangular loss network
Three nodes have integer link capacities $C_{12},C_{13},C_{23}$. Calls between a node pair use either its direct link or the two-link alternative. With unrestricted instantaneous rearrangement of existing calls, counts $n_{12},n_{13},n_{23}$ are feasible exactly when $n_{12}+n_{13}\leq C_{12}+C_{13}$, $n_{12}+n_{23}\leq C_{12}+C_{23}$ and $n_{13}+n_{23}\leq C_{13}+C_{23}$. Necessity follows by counting calls crossing each node cut. For sufficiency, the inequalities allow at most one count to exceed its direct-link capacity. Divert precisely that excess to the other two links; the same inequalities ensure capacity there. The counts thus have the same feasible set as a <fixed routing> <loss network> with one virtual resource at each node, capacity equal to the sum of its two incident physical-link capacities, and each call using its two endpoint resources. With independent <Poisson processes> for arrivals and independent routing-independent <exponential distributions> for holding times, this gives the usual <product-form stationary distribution of a loss network> and exact <Poisson arrivals see time averages> blocking probabilities.
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