Balancing of the C-mu rule by intermediate priorities

Abstract The $$C\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> -rule is well known to be socially optimal in the sense that it minimizes the overall mean waiting costs due to queueing. Yet, this rule is blind to fairness. In particular, it is possible that those with a high cost of wait per unit of time not only enjoy priority over other customers (which is acceptable) but may also end up incurring less waiting costs than those with a corresponding low parameter (which is less acceptable). We suggest a fairer scheme which minimizes the overall cost under the constraint that this anomaly does not exist. It is based on partitioning customers’ classes into leagues, such that absolute priority is granted among the leagues a-la the $$C\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> -rule, while within leagues intermediate priorities, such as accumulated priorities, are used. Toward that end, we revisited some results on such priority schemes and derived some new ones.