Proposition: Two-link concurrent counterexample

Consider a chain of two independent rate-$\lambda$ link generators with ideal storage and instantaneous swapping. If both generators start at time zero, the Bell connection is ready at

Serial generation takes $S_{\mathrm{serial}}={\tau }_1+{\tau }_2$. For $t\ge 0$,

whereas

Their means are $3/(2\lambda )$ and $2/\lambda$. Thus concurrent independent exponential link generation does not imply additive FPP route cost.

Proof. With storage, the first completed pair can wait for the second. Both are available at their maximum completion time. Independence gives the first distribution. Convolution of two exponential densities gives the second. Integrating either survival function gives its stated mean.