Dynamic hierarchical networks represent an architectural strategy for employing adaptive behavior in applications sensitive to highly variable external demands or uncertain internal conditions. The characteristics of such architectures are described, and the significance of adaptive capability is discussed. The necessity for assessing cost/benefit tradeoffs leads to the use of queueing network models. The general model, a network of M/M/1 queues in a random environment, is introduced and then is simplified so that the links may be treated as isolated M/M/1 queues in a random environment. This treatment yields a formula for approximate mean network delay by combining matrix-geometric results (mean queue length and mean delay) for the individual links. Conditions under which the analytic model is considered valid are identified through comparison with a discrete event simulation model. Last, performance of the dynamic hierarchy is compared with that of the static hierarchy. This comparison establishes conditions for which the dynamic architecture enables performance equal or nearly equal to performance of the static architecture.