论文标题
加入最短队列下的负载平衡系统：多种服务器繁殖的渐近造型
Load balancing system under Join the Shortest Queue: Many-Server-Heavy-Traffic Asymptotics
论文作者
论文摘要
我们研究了在多个服务器重型交通状态下加入最短队列（JSQ）下运行的负载平衡系统。如果$ n $是服务器的数量，我们让总服务率和总到达率之间的差额为$ n^{1-α} $，$α> 0 $。我们表明，对于$α> 4 $，平均队列长度的行为与经典的重型交通状态相似。具体而言，我们证明，平均队列长度的分布乘以$ n^{1-α} $收敛到指数随机变量。此外，我们显示出类似于状态空间崩溃的结果。我们为结果提供了两个证明：一种使用单方面的拉普拉斯变换，另一个使用Stein的方法。我们还获得了Wasserstein距离的收敛速度。
We study the load balancing system operating under Join the Shortest Queue (JSQ) in the many-server heavy-traffic regime. If $N$ is the number of servers, we let the difference between the total service rate and the total arrival rate be $N^{1-α}$ with $α>0$. We show that for $α>4$ the average queue length behaves similarly to the classical heavy-traffic regime. Specifically, we prove that the distribution of the average queue length multiplied by $N^{1-α}$ converges to an exponential random variable. Moreover, we show a result analogous to state space collapse. We provide two proofs for our result: one using the one-sided Laplace transform, and one using Stein's method. We additionally obtain the rate of convergence in the Wasserstein's distance.
