Optimal Dynamic Transfer Policies for Parallel Queues with Time-Varying Demand and Convex Holding Costs

The optimal policy partitions the state-space into a well-defined 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, the optimal policy moves the state to the boundary of the no-transfer region, while in the presence of fixed costs, it moves the state to the relative interior.