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. A discrete event simulation model is defined as a basis for cross-validation of the analytic model. Conditions under which the analytic model is considered valid are identified through comparison of the two models. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.