Apparatuses including a test interface circuit that is configured to merge multiple independent traffic streams generated from individual algorithmic pattern generators (APGs) for communication with a memory device over a shared memory interface. The combination of multiple independent traffic streams, each with their own looping sequences and command timings, may generate a large set of random command sequences. The test interface circuit may include an arbiter circuit that merges a first independent traffic stream from a first APG and a second independent traffic stream from a second APG. Each of the first and second independent traffic streams are directed to different semi-independently-accessible portions of the memory device. The memory device may include a hybrid memory cube having independently accessible vaults or a high bandwidth memory device having independently accessible channels, in some examples. The test interface circuit may be included in a built-in self-test engine or in a standalone tester.