In this paper, we present a queueing model for quantum communication networks, a rapidly growing field of research inspired by its technological promise and recent experimental successes. The model consists of a primary queue and a service queue where Bell pairs are formed and stored. The Bell pairs are by nature extremely short-lived rendering the service queue (the quantum queue) much faster than the primary queue. We study the asymptotic behaviour of this multi-scale queueing system utilizing the theory of stochastic averaging principle. We prove a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) for the standard queue averaging the dynamics of the fast service queue. Our proofs are probablistic and rely on the stochastic analysis of Stochastic Differential Equations (SDEs) driven by Poisson Random Measures.

翻译：本文提出了一种量子通信网络的排队模型，该研究领域正因其技术前景与近期实验突破而迅速发展。该模型包含主队列与服务队列，其中贝尔对在此生成与存储。贝尔对本质上具有极短的寿命，导致服务队列（量子队列）的演化速度远快于主队列。我们运用随机平均原理理论研究了该多尺度排队系统的渐近行为。针对通过快速服务队列动态平均得到的标准队列，我们证明了泛函大数定律（FLLN）与泛函中心极限定理（FCLT）。证明过程采用概率方法，并基于泊松随机测度驱动的随机微分方程（SDE）进行随机分析。