  Quantum Internetworking is a recent field that promises numerous interesting
applications, many of which require the distribution of entanglement between
arbitrary pairs of users. This work deals with the problem of scheduling in an
arbitrary entanglement swapping quantum network - often called first generation
quantum network - in its general topology, multicommodity, loss-aware
formulation. We introduce a linear algebraic framework that exploits quantum
memory through the creation of intermediate entangled links. The framework is
then employed to apply Lyapunov Drift Minimization (a standard technique in
classical network science) to mathematically derive a natural class of
scheduling policies for quantum networks minimizing the square norm of the user
demand backlog. Moreover, an additional class of Max-Weight inspired policies
is proposed and benchmarked, reducing significantly the computation cost at the
price of a slight performance degradation. The policies are compared in terms
of information availability, localization and overall network performance
through an ad-hoc simulator that admits user-provided network topologies and
scheduling policies in order to showcase the potential application of the
provided tools to quantum network design.
