Fast-Slow Communication with Endogenous Transport

Abstract

A communication system may convey urgent information through a fast physical stream and more specific information through a slower material stream. In several biological and engineered settings, however, the fast process also changes the transport law of the slow one. We study this architecture under a shared resource constraint, with a strictly increasing concave fast-channel capacity--cost function and a deadline-constrained slow molecular channel. We first characterize the capacity region under separated message routing and message-independent operating-point schedules, and identify the marginal criterion for complementarity rather than competition between the streams. For one-dimensional drift diffusion, we prove that arrival probability before a deadline is strictly log-concave in Péclet number. For a distinguishable-token deadline-erasure channel, any increasing concave transport-actuation law then yields an exact single-crossing theorem: complementarity exists if and only if an initial transport-assistance elasticity exceeds one, the transition is unique when it exists, and the decreasing allocation branch remains the Pareto boundary after convexification. For positive baseline drift and sufficiently strong coupling, a unique critical normalized deadline determines when complementarity disappears. Short- and long-deadline limits clarify the associated temporal regimes. Numerical examples for a finite-frame LTI-Poisson slow channel exhibit analogous allocation behavior with counting noise and intersymbol interference.