Abstract In this paper, we propose a class of approximation algorithms for the max-weight matching (MWM) policy for input-queued switches, called expected 1-APRX. We establish the state space collapse (SSC) result for expected 1-APRX, and characterize its queue length behavior in the heavy-traffic limit. Our results indicate that expected 1-APRX can approximately approach the optimal queue length scaling in the heavy-traffic regime. We further propose an expected 1-APRX based policy, called MWM with adaptive update (MWM-AU), for reducing communication cost due to queue information update. We prove that MWM-AU is throughput optimal and characterize its heavy-traffic limit behavior. Our simulation results demonstrate that the proposed policy can significantly reduce queue update overhead, while maintaining the delay performance comparable to that of MWM.

中文翻译：

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输入队列交换机近似最大权重匹配算法的大流量分析

摘要 在本文中，我们提出了一类用于输入排队交换机的最大权重匹配 (MWM) 策略的近似算法，称为预期 1-APRX。我们为预期的 1-APRX 建立状态空间崩溃 (SSC) 结果，并表征其在大流量限制下的队列长度行为。我们的结果表明，预期的 1-APRX 可以近似地接近大流量情况下的最佳队列长度缩放。我们进一步提出了一种预期的基于 1-APRX 的策略，称为具有自适应更新的 MWM（MWM-AU），用于减少由于队列信息更新引起的通信成本。我们证明 MWM-AU 是吞吐量最优的，并表征了其大流量限制行为。我们的模拟结果表明，所提出的策略可以显着减少队列更新开销，