Diffusion approximation forGI/G/1 controlled queues
Diffusion approximation forGI/G/1 controlled queues
复制标题
GI/G/1 控制队列的扩散近似
DOI：
10.1007/bf01158808
复制
发表时间：
1992
期刊：
影响因子：
1.2
通讯作者：
M. Taksar
中科院分区：
文献类型：
--
作者：
E. V. Krichagina;M. Taksar
考虑了一个调度模型，在该模型中，控制器可以提高服务率。有一个由函数h表示的持有成本和与系数l成正比的增加率的服务成本。当h和l都很小时，系统在繁忙的交通中运行，控制问题可以近似为布朗运动的奇异随机控制问题，即所谓的“反射跟随者”问题。在这个问题中的最优策略是由一个单一的数字z *，使最优过程是一个反射扩散在[0，z*]。为了得到z *，需要求解二阶常微分方程的自由边界问题。对于原问题，当归一化的服务器长度λ sz * 近似最优时，服务率最大化的策略。
A queueing model is considered in which a controller can increase the service rate. There is a holding cost represented by functionh and the service cost proportional to the increased rate with coefficientl. The objective is to minimize the total expected discounted cost.Whenh andl are small and the system operates in heavy traffic, the control problem can be approximated by a singular stochastic control problem for the Brownian motion, namely, the so-called “reflected follower” problem. The optimal policy in this problem is characterized by a single numberz* so that the optimal process is a reflected diffusion in [0,z*]. To obtainz* one needs to solve a free boundary problem for the second order ordinary differential equation. For the original problem the policy which increases to the maximum the service rate when the normalized queue-length exceedsz* is approximately optimal.