论文标题
在模型不确定性下的广义$Cμ$规则的渐近最优性
Asymptotic optimality of the generalized $cμ$ rule under model uncertainty
论文作者
论文摘要
我们考虑使用模型不确定性的重载多类排队控制问题。该模型由$ i $类型的客户和一台服务器组成。在任何时候，决策者（DM）将服务器的努力分配给客户。 DM的目标是最大程度地降低凸持有成本，以说明模型的歧义，即到达和服务率。为此，我们考虑了一个对手玩家，其角色是选择最坏的情况。具体而言，我们假设DM有一个参考概率模型，并且成本函数是由超级人通过两个组件对参考度量的等效概率指标提出的，第一个是预期的保持成本，第二个是对偏离参考模型的逆境参与者的惩罚。惩罚项由一般分歧度量提出。 我们表明，尽管在同等的接受度量下，可能会违反关键负载条件，但对此问题的广义$Cμ$规则在渐近上是最佳的。
We consider a critically-loaded multiclass queueing control problem with model uncertainty. The model consists of $I$ types of customers and a single server. At any time instant, a decision-maker (DM) allocates the server's effort to the customers. The DM's goal is to minimize a convex holding cost that accounts for the ambiguity with respect to the model, i.e., the arrival and service rates. For this, we consider an adversary player whose role is to choose the worst-case scenario. Specifically, we assume that the DM has a reference probability model in mind and that the cost function is formulated by the supremum over equivalent admissible probability measures to the reference measure with two components, the first is the expected holding cost, and the second one is a penalty for the adversary player for deviating from the reference model. The penalty term is formulated by a general divergence measure. We show that although that under the equivalent admissible measures the critically-load condition might be violated, the generalized $cμ$ rule is asymptotically optimal for this problem.
