To effectively support the execution of quantum network applications for multiple sets of user-controlled quantum nodes, a quantum network must efficiently allocate shared resources. We study traffic models for a type of quantum network hub called an Entanglement Generation Switch (EGS), a device that allocates resources to enable entanglement generation between nodes in response to user-generated demand. We propose an on-demand resource allocation algorithm, where a demand is either blocked if no resources are available or else results in immediate resource allocation. We model the EGS as an Erlang loss system, with demands corresponding to sessions whose arrival is modelled as a Poisson process. To reflect the operation of a practical quantum switch, our model captures scenarios where a resource is allocated for batches of entanglement generation attempts, possibly interleaved with calibration periods for the quantum network nodes. Calibration periods are necessary to correct against drifts or jumps in the physical parameters of a quantum node that occur on a timescale that is long compared to the duration of an attempt. We then derive a formula for the demand blocking probability under three different traffic scenarios using analytical methods from applied probability and queueing theory. We prove an insensitivity theorem which guarantees that the probability a demand is blocked only depends upon the mean duration of each entanglement generation attempt and calibration period, and is not sensitive to the underlying distributions of attempt and calibration period duration. We provide numerical results to support our analysis. Our work is the first analysis of traffic characteristics at an EGS system and provides a valuable analytic tool for devising performance driven resource allocation algorithms.

翻译：为有效支持多组用户控制量子节点的量子网络应用执行，量子网络必须高效分配共享资源。我们研究了一种称为纠缠生成交换机（EGS）的量子网络枢纽的流量模型，该设备通过分配资源以响应用户需求实现节点间纠缠生成。我们提出一种按需资源分配算法：若无可用资源则阻塞需求，否则立即分配资源。我们将EGS建模为爱尔朗损失系统，需求对应会话到达且服从泊松过程。为反映实际量子交换机的运行，我们的模型捕捉了以下场景：资源分配用于批量纠缠生成尝试，其间可能穿插量子网络节点的校准周期。校准周期用于校正量子节点物理参数在时间尺度上（相对于单次尝试时长）发生的漂移或跳变。随后，我们运用应用概率与排队论的分析方法，推导出三种不同流量场景下的需求阻塞概率公式。我们证明了一个不敏感性定理，该定理保证需求阻塞概率仅取决于每次纠缠生成尝试与校准周期的平均时长，而对尝试时长与校准周期时长的具体分布不敏感。我们提供了数值结果以支持分析。本研究首次对EGS系统的流量特性进行分析，为设计性能驱动的资源分配算法提供了有价值的分析工具。