Hierarchical distributed search, locating a data pattern, or signature, across a tree-structured collection of files, underlies distributed index traversal, deep packet inspection and sequence alignment. A practitioner must decide how much parallelism to employ: scan each layer sequentially, fan out within subtrees, or launch the whole tree at once. Existing analyses answer this only partially: they characterize every node by the statistics of a signature-holding file and, for multi-signature files, need quantities revealed only at run time. We develop a probabilistic framework predicting the completion time of five search strategies, spanning sequential to full-tree parallelism, before any file is read. Node scan times are modeled as a mixture over signature presence, layer times as order statistics, and parallel subtree scans by extreme-value arguments; when signature counts are known, occupancy under capacity constraints is treated by generating functions. Each performance formula carries an exactness label: exact (or exact-in-regime), plug-in, asymptotic or bound, with each approximation quantified against Monte Carlo simulation and its regime identified. A multicore prototype reproduces the coarse separation between full-tree, layer- and subtree-level parallelism, but shows that synchronization overhead can erase the predicted separation between close strategies. The framework delivers a priori completion-time predictions with explicit accuracy regimes and negligible computational cost, the design example evaluated in under a millisecond; these timing models can support subsequent resource-cost optimization.

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