The Delay-Capacity product for store-and-forward communication networks: Tree networks

A store-and-forward communication network under a maximal message delay criterion is considered. It is shown that the overall channel capacityC and the associated minimal maximal delayγ, as well as the maximal delayγ and the associated minimal overall capacityC, are characterized by a unique Delay-Capacity (γC) product number. The latter is related to a Delay-Capacity product (γC)⁺ number, uniquely determined solely by the topological structure of the communication network. Basic characteristics of the optimal delay and capacity assignment, a useful algoritm for the calculation of (γC)⁺ and simple upper and lower bounds on (γC)⁺, are derived for store-and-forward tree networks. Synthesis considerations and applications to hierarchical communication networks are noted.