We consider a quantum switch with a finite number of quantum memory registers that aims to serve multipartite entanglement requests among $N$ users. We propose scheduling policies that aim to optimize the average number of requests served per unit time by efficiently utilizing the switch's available memory. To measure the performance of the scheduling policies, we employ the newly introduced metric of age of entanglement establishment (AoEE). We formulate the scheduling problem in a restless multi-armed bandit (RMAB) framework. We show that the scheduling of entanglement requests is indexable. Subsequently, we find a closed-form expression of the Whittle index for all possible request-age pairs. By modeling the Whittle index of each request as its reward and its cardinality as its cost, we formulate the memory-constrained scheduling problem as a $0$-$1$ knapsack problem and solve it via dynamic programming. Furthermore, we consider two low-complexity sequential greedy policies that leverage two different modified Whittle indices.

翻译：我们考虑一台配备有限数量量子存储器寄存器的量子交换机，旨在服务于 $N$ 个用户间的多部分纠缠请求。我们提出了调度策略，通过高效利用交换机可用存储器，优化单位时间内服务请求的平均数量。为衡量调度策略性能，我们采用新引入的纠缠建立年龄（AoEE）指标。我们基于非稳态多臂老虎机（RMAB）框架构建调度问题，并论证纠缠请求的调度具有可索引性。随后，我们给出了所有可能请求-年龄对的Whittle索引闭式表达式。通过将每个请求的Whittle索引建模为奖励、基数建模为成本，我们将受存储器约束的调度问题转化为 $0$-$1$ 背包问题，并采用动态规划求解。此外，我们提出了两种利用不同修正Whittle索引的低复杂度顺序贪婪策略。