Unintended consequences of optimizing a queue discipline for a service level defined by a percentile of the waiting time

In service systems, the service level is often represented by a percentile of the waiting time. This creates an incentive to optimize the queue discipline. For this purpose, in an M/M/s queue setting, we prove that the optimal discipline gives priority to the oldest customer who has waited less than the acceptable waiting time. Next, we derive explicitly the performance measures. Finally, we show that although this discipline may reduce staffing costs, it leads to excessive wait for non-prioritized customers.