Simplified Control Problems for Multiclass Many-Server Queueing Systems
Simplified Control Problems for Multiclass Many-Server Queueing Systems
复制标题
多类多服务器排队系统的简化控制问题
DOI：
10.1287/moor.1090.0404
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
G. Shaikhet
中科院分区：
文献类型：
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作者：
R. Atar;A. Mandelbaum;G. Shaikhet
我们考虑调度和路由控制问题的排队模型与I客户类和J服务器池，每个由许多统计相同，指数服务器。客户需要一个单一的服务，可以由服务器从其中一个池中执行;服务率μij ≥ 0，这取决于客户的类i和服务器的池j，客户可以在等待服务时放弃系统。在Halfin和Whitt的重交通区中，这些问题形式上等价于I维扩散控制问题。我们分析扩散控制问题是两种特殊情况。首先，当服务率仅依赖于池（μij = μj）时，扩散控制问题与单类模型的扩散控制问题类似（但又不同），从而大大降低了问题的复杂性.其次，当服务率只依赖于类（μij = μi），扩散控制问题被证明是等价的单池模型的扩散控制问题，以前已经研究过的问题。在第一种情况下，我们还建立了严格的关系之间的扩散控制问题和扩散控制问题，显示的政策的扩散模型，基于一个常微分方程的Hamilton-Jacobi-Bellman型，是渐近最优的。
We consider scheduling and routing control problems for queueing models with I customer classes and J server pools, each consisting of many statistically identical, exponential servers. Customers require a single service that can be performed by a server from one of the pools; the service rate is μij ≥ 0, which depends on the customer's class i and the server's pool j, and customers can abandon the system while waiting to be served. In the heavy traffic regime of Halfin and Whitt, these problems are formally equivalent to I-dimensional diffusion control problems. We analyze the diffusion control problems is two special cases. First, when the service rates depend only on the pool (μij = μj), the diffusion control problem is shown to be similar to (but distinct from) the diffusion control problem for a single class model, which greatly reduces the complexity of the problem. Second, when the service rates depend only on the class (μij = μi), the diffusion control problem is shown to be equivalent to a diffusion control problem for a single pool model, a problem that has previously been studied. In the first case, we also establish a rigorous relation between the queueing control problem and the diffusion control problem, showing that a policy for the queueing model, based on an ordinary differential equation of Hamilton-Jacobi-Bellman type, is asymptotically optimal.