论文标题
匹配队列与量子开关中的放弃：稳定性和吞吐量分析
Matching Queues with Abandonments in Quantum Switches: Stability and Throughput Analysis
论文作者
论文摘要
受量子开关的启发，我们考虑了一个带有两类到达的离散时间多路匹配系统：两个节点之间的纠缠对量子对的请求，每个节点的量子位量子都可用于服务请求。该模型的一个重要特征是Qubits DecoHere，随着时间的流逝如此放弃。与基于经典服务器的排队模型相反，排队，无服务器多路匹配和（可能相关的）放弃的组合使分析成为一个具有挑战性的问题。本文的主要重点是研究一个简单的系统，该系统由两种类型的请求和三种类型的Qubits组成，在最大重量策略下运行。 在这种情况下，我们通过采用两次刻度流体限制来掌握放弃，从而表征了最大重量策略下的稳定区域。特别是，我们表明Max-jight是吞吐量的最佳选择，并且可以实现比在无限反向召集的请求时通过非上调策略实现的吞吐量大。此外，尽管使用了最大重量策略，但我们表明系统中可能存在违反直觉的行为：即使整个系统稳定，队列最长的请求也可以在一段时间内积极漂移。
Inspired by quantum switches, we consider a discrete-time multi-way matching system with two classes of arrivals: requests for entangled pair of qubits between two nodes, and qubits from each node that can be used to serve the requests. An important feature of this model is that qubits decohere and so abandon over time. In contrast to classical server-based queueing models, the combination of queueing, server-less multi-way matching, and (potentially correlated) abandonments make the analysis a challenging problem. The primary focus of this paper is to study a simple system consisting of two types of requests and three types of qubits operating under a Max-Weight policy. In this setting, we characterize the stability region under the Max-Weight policy by adopting a two-time scale fluid limit to get a handle on the abandonments. In particular, we show that Max-Weight is throughput optimal and that it can achieve throughputs larger than the ones that can be achieved by non-idling policies when the requests are infinitely backlogged. Moreover, despite the use of the Max-Weight policy, we show that there can be a counter-intuitive behavior in the system: the longest requests queue can have a positive drift for some time even if the overall system is stable.
