Infinite Horizon Average Optimality of the N-network Queueing Model in the Halfin-Whitt Regime
Infinite Horizon Average Optimality of the N-network Queueing Model in the Halfin-Whitt Regime
复制标题
Halfin-Whitt 机制下 N 网络排队模型的无限时域平均最优性
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
G. Pang
中科院分区：
文献类型：
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作者：
A. Arapostathis;G. Pang
研究了由两个客户类和两个服务器池组成的n -网络排队系统在平均（遍历时）准则下的无限视界最优控制问题。我们考虑了三个控制目标：1)最小化排队（和空闲）成本，2)最小化排队成本，同时对每个服务器池的空闲施加约束，以及3)最小化排队成本，同时要求空闲的公平性。运行代价可以是任何不超过多项式增长的非负凸函数。对于这三个问题，我们建立了渐近最优性，即扩散尺度状态过程的值函数收敛到控制扩散极限的相应值。我们还提出了一种简单的状态依赖的优先级调度策略，在该策略下，扩散尺度的状态过程在Halfin-Whitt域中是几何遍历的，并给出了一些关于平均经验测度的收敛性的结果。
We study the infinite horizon optimal control problem for N-network queueing systems, which consist of two customer classes and two server pools, under average (ergodic) criteria in the Halfin–Whitt regime. We consider three control objectives: 1) minimizing the queueing (and idleness) cost, 2) minimizing the queueing cost while imposing a constraint on idleness at each server pool, and 3) minimizing the queueing cost while requiring fairness on idleness. The running costs can be any nonnegative convex functions having at most polynomial growth. For all three problems we establish asymptotic optimality, namely, the convergence of the value functions of the diffusion-scaled state process to the corresponding values of the controlled diffusion limit. We also present a simple state-dependent priority scheduling policy under which the diffusion-scaled state process is geometrically ergodic in the Halfin–Whitt regime, and some results on convergence of mean empirical measures which facilitate the proofs.