  Given the diverse array of physical systems available for quantum computing
and the absence of a well-defined quantum internet protocol stack, the design
and optimisation of quantum networking protocols remain largely unexplored. To
address this, we introduce an approach that facilitates the establishment of
paths capable of delivering end-to-end fidelity above a specified threshold,
without requiring detailed knowledge of the quantum network properties, which
we call the 'grey box approach'. In this study, we define algorithms that are
specific instances of this approach and evaluate them in comparison to Dijkstra
shortest path algorithm and a fully knowledge-aware algorithm through
simulations. Our results demonstrate that one of the grey box algorithms
consistently outperforms the other methods in delivering paths above the
fidelity threshold, across various network topologies and the number of
source-destination pairs involved, while maintaining significant levels of
fairness among the users and being robust to inaccurate estimations of the
expected end-to-end fidelity.
