Storage and Transport Capacity Design for a Self-Reliable Two-Node Stochastic Resource System
For operators of distributed resource systems (e.g., energy or water networks), this provides a theoretical framework to jointly design storage and transport capacities under uncertainty.
This paper studies a two-node stochastic resource system with uncertain supply and demand, aiming to keep resource levels within limits with high probability. It characterizes minimum storage, optimal transport policy, and the storage-transport trade-off, finding a critical transport-capacity threshold for full risk pooling that decreases with longer horizons.
We study a two-node stochastic resource system operating over a finite horizon. Each node experiences uncertain supply and demand and is equipped with finite storage. The objective is to ensure that resource levels remain within prescribed limits with high probability. To this end, we formulate a chance-constrained capacity-design problem in which resources can be exchanged through a capacity-limited transport link. We characterize the minimum storage required at each node, derive the optimal transport policy, and quantify the trade-off between storage and transport capacities. Our results show the existence of a critical transport-capacity threshold that enables full risk pooling between the nodes. Moreover, this threshold decreases with the operating horizon, implying that full-pooling performance can be achieved with progressively smaller transport capacity over longer horizons.