Optimality-Induced Stabilization in Stochastic Networked Resource Allocation Systems

Large-scale operational systems such as transportation, logistics, and distributed service networks must allocate limited resources under stochastic demand while maintaining stable system performance. These systems are often modeled as stochastic network optimization problems in which resource allocation decisions are chosen to minimize congestion or operational costs subject to shared capacity constraints. While classical scheduling policies enforce stability through explicitly designed control rules, many real-world decision systems rely primarily on cost-driven optimization mechanisms. This paper investigates whether cost-minimizing policies can inherently guarantee stability in stochastic networked resource allocation systems. We study a class of controlled Markov decision processes with convex capacity regions and coercive congestion cost functions. We prove that when the exogenous demand vector lies strictly within the interior of the capacity region, every optimal stationary policy for the discounted problem necessarily induces a negative Foster–Lyapunov drift outside a compact set, implying positive recurrence of the system state. Conversely, when demand exceeds the capacity boundary, no feasible policy can stabilize the system, establishing the convex capacity region as the maximal stabilizable demand set. The theoretical results are illustrated through computational experiments on a multi-terminal logistics network with stochastic arrivals and shared routing capacities. Simulation results reveal a clear phase transition between stable and unstable regimes and demonstrate that convex congestion-based optimization policies can reproduce the stabilizing behavior of classical scheduling rules while achieving lower operational costs. These findings highlight a structural link between economic optimization and stochastic stability in networked operational systems.