  We provide the first analytical expressions for the expected waiting time of
high-priority customers in the delayed APQ by exploiting a classical
conservation law for work-conserving queues. Additionally, we describe an
algorithm to compute the expected waiting times of both low-priority and
high-priority customers, which requires only the truncation of sums that
converge quickly in our experiments. These insights are used to demonstrate how
the accumulation rate and delay level should be chosen by health care
practitioners to optimize common key performance indicators (KPIs). In
particular, we demonstrate that for certain nontrivial KPIs, an accumulating
priority queue with a delay of zero is always preferable. Finally, we present a
detailed investigation of the quality of an exponential approximation to the
high-priority waiting time distribution, which we use to optimize the choice of
queueing parameters with respect to both classes' waiting time distributions.
