The Adaptive MaxWeight policy achieves optimal throughput for switches with nonzero reconfiguration delay and has been shown to have good delay performance in simulation. In this paper, we analyze the queue length behavior of a switch with nonzero reconfiguration delay operating under the Adaptive MaxWeight. We first show that the Adaptive MaxWeight policy exhibits a weak state space collapse behavior in steady state, which can be viewed as an inheritance of a similar property of the MaxWeight policy in a switch with zero reconfiguration delay. The weak state space collapse result is then utilized to obtain an asymptotically tight bound on an expression involving the steady-state queue length and the probability of reconfiguration for the Adaptive MaxWeight policy in the heavy traffic regime. We then derive the relation between the expected schedule duration and the steady-state queue length through Lyapunov drift analysis and characterize bounds for the expected steady-state queue length. While the resulting queue length bounds are not asymptotically tight, they suggest an approximate queue length scaling behavior, which approaches the optimal scaling with respect to the traffic load and the reconfiguration delay when the hysteresis function of the Adaptive MaxWeight policy approaches a linear function.

自适应MaxWeight策略可为具有非零重新配置延迟的交换机实现最佳吞吐量，并且在仿真中已显示出良好的延迟性能。在本文中，我们分析了在自适应最大权重下运行的具有非零重配置延迟的交换机的队列长度行为。我们首先显示自适应MaxWeight策略在稳定状态下表现出弱状态空间崩溃行为，可以将其视为具有零重配置延迟的交换机中MaxWeight策略的类似属性的继承。然后，利用弱状态空间崩溃结果在表达式上获得渐近紧边界，该表达式涉及稳态队列长度和繁忙交通状况下Adaptive MaxWeight策略的重新配置概率。然后，我们通过Lyapunov漂移分析得出预期调度持续时间与稳态队列长度之间的关系，并描述预期稳态队列长度的界限。尽管所得的队列长度边界不是渐近严格的，但它们提出了近似的队列长度缩放行为，当Adaptive MaxWeight策略的磁滞函数接近线性函数时，该行为接近于流量负载和重新配置延迟的最佳缩放。