论文标题
对数的重型交通误差在广义开关和负载平衡系统中的界限
Logarithmic Heavy Traffic Error Bounds in Generalized Switch and Load Balancing Systems
论文作者
论文摘要
通过在无线网络，云计算，数据中心等中应用的动机，在各种渐近方案下的文献中已经研究了随机处理网络。在繁重的交通状态下，稳态平均队列长度被证明为$ o（\ frac {1}ε）$，其中$ε$是重型交通参数，在极限中为零。本文的重点是在预赛系统上获得队列长度的范围，从而确立了与交通繁忙的收敛速度。特别是，我们研究了在MaxWeight算法下运行的广义开关模型，并且我们表明，预序系统的平均队列长度仅为$ o \ left（\ log \ left（\ frac {1}ε\ right）\ right）$远离其重量限制。即使不满足所谓的完整资源池（CRP）条件，我们也要这样做。当满足CRP条件时，我们还表明，最大算法在$ o \ left（\ log \ left（\ frac {1}ε\ right）\ right）$）$中。最后，我们在加入最短队列路由算法下运行的负载平衡系统中获得了类似的结果。
Motivated by application in wireless networks, cloud computing, data centers etc, Stochastic Processing Networks have been studied in the literature under various asymptotic regimes. In the heavy-traffic regime, the steady state mean queue length is proved to be $O(\frac{1}ε)$ where $ε$ is the heavy-traffic parameter, that goes to zero in the limit. The focus of this paper is on obtaining queue length bounds on prelimit systems, thus establishing the rate of convergence to the heavy traffic. In particular, we study the generalized switch model operating under the MaxWeight algorithm, and we show that the mean queue length of the prelimit system is only $O\left(\log \left(\frac{1}ε\right)\right)$ away from its heavy-traffic limit. We do this even when the so called complete resource pooling (CRP) condition is not satisfied. When the CRP condition is satisfied, in addition, we show that the MaxWeight algorithm is within $O\left(\log \left(\frac{1}ε\right)\right)$ of the optimal. Finally, we obtain similar results in load balancing systems operating under the join the shortest queue routing algorithm.
