  We consider the problem of load balancing in parallel queues by transferring
customers between them at discrete points in time. Holding costs accrue as
customers wait in the queue, while transfer decisions incur both fixed (setup)
and variable costs proportional to the number and direction of transfers. Our
work is primarily motivated by inter-facility patient transfers between
hospitals during a surge in demand for hospitalization (e.g., during a
pandemic). By analyzing an associated fluid control problem, we show that under
fairly general assumptions including time-varying arrivals and convex
increasing holding costs, the optimal policy in each period partitions the
state-space into a well-defined $\textit{no-transfer region}$ and its
complement, such that transferring is optimal if and only if the system is
sufficiently imbalanced. In the absence of fixed transfer costs, an optimal
policy moves the state to the no-transfer region's boundary; in contrast, with
fixed costs, the state is moved to the no-transfer region's relative interior.
We further leverage the fluid control problem to provide insights on the
trade-off between holding and transfer costs, emphasizing the importance of
preventing excessive idleness when transfers are not feasible in
continuous-time. Using simulation experiments, we investigate the performance
and robustness of the fluid policy for the stochastic system. In particular,
our case study calibrated using data during the pandemic in the Greater Toronto
Area demonstrates that transferring patients between hospitals could result in
up to 27.7% reduction in total cost with relatively few transfers.
