A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic
A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic
复制标题
大交通量纵横交错网络渐近最优控制的大偏差方法
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Arka P. Ghosh
中科院分区：
文献类型：
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作者：
A. Budhiraja;Arka P. Ghosh
在这项工作中，我们研究了一个众所周知的多类排队网络的渐近最优控制问题，称为“交叉网络”，在重型运输中。我们考虑了指数级的到达间隔和服务时间，线性的持有成本和无限的水平贴现成本准则。在合适的参数范围内，Martins， Shreve和sononer[11]用粘度解方法对这一问题进行了详细的研究。在这项工作中，使用布朗控制问题的路径解，我们使用[5,1]中引入的大偏差思想，对该问题（具有与[11]相同的参数区）进行了基本和透明的处理。得到了一个阈值型的渐近最优调度策略。该证明具有独立的意义，因为它是为数不多的给出具有一维以上工作负载过程的网络控制策略渐近最优性的结果之一。
In this work we study the problem of asymptotically optimal control of a well known multi-class queuing network, referred to as the \crisscross network", in heavy tra‐c. We consider exponential inter-arrival and service times, linear holding cost and an inflnite horizon discounted cost criterion. In a suitable parameter regime, this problem has been studied in detail by Martins, Shreve and Soner [11] using viscosity solution methods. In this work, using the pathwise solution of the Brownian Control Problem, we present an elementary and transparent treatment of the problem (with the identical parameter regime as in [11]) using large deviation ideas introduced in [5, 1]. We obtain an asymptotically optimal scheduling policy which is of threshold type. The proof is of independent interest since it is one of the few results which gives the asymptotic optimality of a control policy for a network with a more than one dimensional workload process.