On the Equivalence of Shannon Capacity and Stable Capacity in Networks with Memoryless Channels

An equivalence result is established between the Shannon capacity and the stable capacity of communication networks. Given a discrete-time network with memoryless, time-invariant, discrete-output channels, it is proved that the Shannon capacity equals the stable capacity. The results treat general demands (e.g., multiple unicast demands) and apply even when neither the Shannon capacity nor the stable capacity is known for the given demands. The result also generalize from discrete-alphabet channels to Gaussian channels.