Top-K queries are an established heuristic in information retrieval. This paper presents an approach for optimal tiered storage allocation under stream processing workloads using this heuristic: those requiring the analysis of only the top-$K$ ranked most relevant, or most interesting, documents from a fixed-length stream, stream window, or batch job. In this workflow, documents are analyzed relevance with a user-specified interestingness function, on which they are ranked, the top-$K$ being selected (and hence stored) for further processing. This workflow allows human in the loop systems, including supervised machine learning, to prioritize documents. This scenario bears similarity to the classic Secretary Hiring Problem (SHP), and the expected rate of document writes, and document lifetime, can be modelled as a function of document index. We present parameter-based algorithms for storage tier placement, minimizing document storage and transport costs. We show that optimal parameter values are a function of these costs. It is possible to model application IO behaviour a priori for this class of workloads. When combined with tiered storage, the tractability of the probabilistic model of IO makes it easy to optimize tier allocation, yielding simple analytic solutions. This contrasts with (often complex) existing work on tiered storage optimization, which is either tightly coupled to specific use cases, or requires active monitoring of application IO load (a reactive approach) -- ill-suited to long-running or one-off operations common in the scientific computing domain.We validate our model with a trace-driven simulation of a bio-chemical model exploration, and give worked examples for two cloud storage case studies.