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Approximate analytical queuing network models for expected message packet delay in 2-level and 3-level hierarchical ring interconnection networks (INs) are developed. A major class of traffic carried by these INs consists of cache line transfers between processor caches and remote memory modules in shared-memory multiprocessors. Such traffic consists of short, fixed-length messages; they can be conveniently transported by the slotted-ring transmission technique which is studied here. The packet delay results derived from the models are shown to be quite accurate when checked against a simulation study. As well as facilitating analysis, the analytical models can be used to determine optimal sizes for the rings at different levels in the hierarchy, where optimality is in terms of minimizing average packet delay.