This paper examines queuing problems in which agents can be ordered according to some exogenous priority structure. We propose a family of allocation rules that achieve both economic efficiency, and respect of the priority relations. This family contains the well-established minimal transfer rule (Maniquet 2003), as well as the priority transfer rule, a new rule we introduce in this paper. Our theoretical results are two-folds. First, we provide an axiomatic characterization of the priority transfer rule. Second, we establish some connections between the family of allocation rules introduced for queuing problems and a new family of solutions for cooperative TU-games that we call the q-Priority Shapley values.

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