AI 中文总结
该研究针对含多作业类、服务器的随机处理网络，构建近似布朗控制问题（BCP），将其数值解转化为接近最优的可执行控制策略，性能优于等效工作量方法。
AI 中文摘要
我们考虑一个具有m个作业类或缓冲区、部分类别的外生输入流、n个处理活动和p个服务器的处理网络模型。每个活动要么是指定服务器处理指定类别的作业，要么是虚构的输入服务器交付指定类别的作业；作业在完成服务后以马尔可夫方式改变类别。标准多类排队网络（作业类与活动一一对应）是该模型的特例，但本通用模型允许对给定类别采用两种或多种处理方式，且系统管理者可自行决定拒绝部分或全部输入流。成本为线性形式：系统中每个类别i的作业每单位时间的持有成本，以及每个类别i到达被拒绝时的拒绝惩罚（i=1,…,m）。系统管理者需做出输入控制、作业路由和服务顺序决策，以最小化无限时间范围内的期望折现成本。我们构建了一个近似布朗控制问题（BCP），其状态空间为m维非负卦限；控制是基于动态状态观测从有界多面体集中选取的漂移向量。利用最新开发的计算方法，BCP可在至少m=50的维度上进行数值求解，我们还说明了如何将该数值解转化为原始排队系统的可执行控制策略。过往关于重负载扩散近似的研究表明，该策略在重负载参数 regime 中接近最优，数值示例也支持这一猜想。我们还讨论了该策略相较于本团队过往研究中采用的替代方法的优势，替代方法用低维“等效工作量 formulation”替代BCP，虽计算高效但难以在原始网络中解释。
英文摘要
We consider a processing network model with $m$ job classes or buffers, exogenous input flows into some classes, $n$ processing activities, and $p$ servers. Each activity is either a specified server processing jobs of a specified class, or a fictional input server delivering jobs of a specified class; jobs change class in Markovian fashion after completing service. A standard multiclass queueing network, with its one-to-one correspondence between job classes and activities, is a special case, but our general model allows two or more ways to process a given class, and some or all input flows may be turned away at the system manager's discretion. Costs are linear: a holding cost per time unit for each class $i$ job in the system, and a rejection penalty for each class $i$ arrival denied access $(i=1,\ldots,m)$. The system manager makes input control, job routing, and order-of-service decisions to minimize expected discounted costs over an infinite horizon. We formulate an approximating Brownian control problem (BCP) whose state space is the $m$-dimensional nonnegative orthant; control is a drift vector chosen from a bounded polyhedral set, based on dynamic state observations. Using recently developed computational methods, the BCP can be solved numerically in dimensions up to at least $m=50$, and we explain how the numerical solution is translated into an implementable control policy for the queueing system of original interest. Previous work on heavy traffic diffusion approximations suggests that this policy is nearly optimal in the heavy traffic parameter regime, and numerical examples support that conjecture. We also discuss its advantage over an alternative approach, featured in our previous work, where the BCP is replaced by a lower-dimensional "equivalent workload formulation" that is computationally efficient but difficult to interpret in the network of original interest.
