论文标题
与高斯输入相关的排队的无环网络的大偏差
Large deviations for acyclic networks of queues with correlated Gaussian inputs
论文作者
论文摘要
我们考虑具有异质处理速率的单人队列的无环网络。假定每个队列都是通过大量i.i.d的叠加来喂养的。高斯工艺具有固定的增量和正漂移，可以在不同的队列中相关。从每个服务器出发的工作流进行确定性拆分，并根据固定的路由矩阵将其路由到邻居，其中一小部分使网络完全离开。 我们研究网络中任何给定节点的稳态队列长度的概率的指数衰减率高于任何固定阈值，也称为“溢出概率”。特别是，我们首先利用Schilder的样品路径大偏差定理，以获得该指数衰减速率极限的一般下限，因为高斯过程的数量流向无穷大。然后，我们表明该下限在其他技术条件下紧绷。最后，我们表明，如果输入过程的不同队列是非连接的，非短距离依赖性的分数布朗尼动作，并且处理速率足够大，则队列的渐近指数衰减速率与孤立的排队与适当的高斯输入相吻合。
We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive drifts, which can be correlated across different queues. The flow of work departing from each server is split deterministically and routed to its neighbors according to a fixed routing matrix, with a fraction of it leaving the network altogether. We study the exponential decay rate of the probability that the steady-state queue length at any given node in the network is above any fixed threshold, also referred to as the "overflow probability". In particular, we first leverage Schilder's sample-path large deviations theorem to obtain a general lower bound for the limit of this exponential decay rate, as the number of Gaussian processes goes to infinity. Then, we show that this lower bound is tight under additional technical conditions. Finally, we show that if the input processes to the different queues are non-negatively correlated, non short-range dependent fractional Brownian motions, and if the processing rates are large enough, then the asymptotic exponential decay rates of the queues coincide with the ones of isolated queues with appropriate Gaussian inputs.
