大规模缓冲系统的随机最长队列优先调度
Randomized longest-queue-first scheduling for large-scale buffered systems
摘要：
通过建立新的平均场极限定理，我们发展了随机最长队列优先调度算法的并行排队系统的扩散近似作为缓冲区的数量$n\to\infty$。我们实现这一点，允许采样缓冲区的数量$d=d(n)$依赖于缓冲区的数量$n$，这产生了一个渐进的“解耦”的队列长度的过程。我们通过模拟实验表明，所得到的近似是准确的，即使是中等值的$n$和$d(n)$。据我们所知，我们是第一个推导出扩散近似的大缓冲区平均场制度中的一个扩散系统。我们的缩放思想的另一个值得注意的特点是，随机最长队列优先算法模拟最长队列优先算法，但在计算上更有吸引力。系统性能作为$d(n)$的函数的分析是由我们的极限定理中的多尺度性质促进的：我们研究的各种过程具有不同的空间标度。这使我们能够显示性能和复杂性的随机最长队列优先调度算法之间的权衡。
英文摘要：
We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing the number of sampled buffers $d=d(n)$ to depend on the number of buffers $n$, which yields an asymptotic `decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of $n$ and $d(n)$. To our knowledge, we are the first to derive diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized longest-queue-first algorithm emulates the longest-queue-first algorithm, yet is computationally more attractive. The analysis of the system performance as a function of $d(n)$ is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized longest-queue-first scheduling algorithm.
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