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We provide the first analytical expressions for the expected waiting time ofhigh-priority customers in the delayed APQ by exploiting a classicalconservation law for work-conserving queues. Additionally, we describe analgorithm to compute the expected waiting times of both low-priority andhigh-priority customers, which requires only the truncation of sums thatconverge quickly in our experiments. These insights are used to demonstrate howthe accumulation rate and delay level should be chosen by health carepractitioners to optimize common key performance indicators (KPIs). Inparticular, we demonstrate that for certain nontrivial KPIs, an accumulatingpriority queue with a delay of zero is always preferable. Finally, we present adetailed investigation of the quality of an exponential approximation to thehigh-priority waiting time distribution, which we use to optimize the choice ofqueueing parameters with respect to both classes' waiting time distributions.

High-Priority Expected Waiting Times in the Delayed Accumulating Priority Queue with Applications to Health Care KPIs