Large-scale join-idle-queue system with general service times
Large-scale join-idle-queue system with general service times
复制标题
服务时间一般的大型加入空闲队列系统
DOI：
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发表时间：
2016
影响因子：
1
通讯作者：
A. Stolyar
中科院分区：
文献类型：
--
作者：
S. Foss;A. Stolyar
考虑具有 $n$ 个相同服务器的并行服务器系统。服务时间分布具有有限均值 $1/mu$，但除此之外是任意的。到达的客户在到达后立即被路由到其中一台服务器。研究了加入空闲队列路由算法，在该算法下，到达的客户被发送到空闲服务器（如果可用），否则被发送到随机统一选择的服务器。我们考虑渐近状态，其中 $n oinfty$ 且客户输入流量为 $lambda n$。在 $lambda/mu<1/2$ 的条件下，我们证明，当 $n oinfty$ 时，（适当缩放的）平稳分布序列集中在自然平衡点，占用服务器的比例恒定等于 $lambda/mu$。特别是，这意味着到达客户等待服务的稳态概率消失了。
A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival. Join-Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where $n oinfty$ and the customer input flow rate is $lambda n$. Under the condition $lambda/mu<1/2$, we prove that, as $n oinfty$, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant equal $lambda/mu$. In particular, this implies that the steady-state probability of an arriving customer waiting for service vanishes.