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 abandonment 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 (dubbed the W-topology) 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 its stability region is larger than the convex hull of the throughputs that can be achieved by non-idling policies when the requests are infinitely backlogged. Moreover, despite the use of a policy that prioritizes the largest requests queue, we show that there can be a counterintuitive behavior in the system: the longest requests queue can have a positive drift for some time even if the overall system is stable.
翻译:在量子开关的启发下,我们认为一个离散时间的多路匹配系统与两类抵达者相匹配:在两个节点和每个节点中可以用于满足请求的QQ&B的要求,以及每个节点的qubit的要求。这个模型的一个重要特征是qubts decothere, 并因此随着时间的推移而放弃。与传统的基于服务器的排队模式相比,排队、服务器无服务器的多路匹配和放弃的组合使得分析成为一个具有挑战性的问题。本文件的主要重点是研究一个简单系统,由两种类型的请求和三种qubits(按W-toplogy)组成,在最大节点政策下运行。在这种环境下,我们通过采用两个比例的流体流体限制来控制放弃。特别是,我们显示,Max-Weight是透视最优化的,其稳定性区域比通过非递增政策可以达到的方位体积体积要大得多,而当请求是无限的排层政策时,我们也可以在最慢的列队列中显示一个稳定的递制。