论文标题
单个服务器等待时间过程的入学控制
Admission Control for A Single Server Waiting Time Process in Heavy Traffic
论文作者
论文摘要
我们解决了来自Lee和Weerasinghe（2011）的沉重流量中的单个服务器队列控制问题（QCP）。国家过程代表所提供的等待时间，客户到达具有州依赖的强度，并且客户的服务和耐心时间是I.I.D，并具有一般分布。我们介绍了无限 - 马折扣成本功能的功能，该功能由控制成本产生的控制成本和闲置成本的罚款。我们的主要目标是考虑到QCP，考虑到不平凡的控制成本以及由于等待时间的控制机制而产生的非侵略成本功能。在轻度假设下，QCP的繁重交通限制产生了一个随机控制问题，该问题由扩散过程描述，我们称之为扩散控制问题（DCP）。我们通过结合Legendre-Fenchel变换和正式的Hamilton-Jacobi-Bellman（HJB）方程来找到对关联DCP的最佳控制。然后，我们``将这种最佳策略转换为QCP，我们获得了渐近的最佳策略。除了理论结果外，我们还研究了增强算法（一种增强学习方法（RL）方法），用于解决最近文献动机的随机控制。我们从理论结果和数据驱动算法中强调了模拟的优点和局限性。
We address a single server queue control problem (QCP) in heavy traffic originating from Lee and Weerasinghe (2011). The state process represents the offered waiting time, the customer arrival has a state-dependent intensity, and the customers' service and patience times are i.i.d with general distributions. We introduce an infinite-horizon discounted cost functional consisting of a control cost generated from the use of control and a penalty for idleness cost. Our primary goal is to tackle the QCP, taking into account a non-trivial control cost and a non-increasing cost function resulting from the control mechanisms in the waiting time. Under mild assumptions, the heavy traffic limit of the QCP yields a stochastic control problem described by a diffusion process, which we call a diffusion control problem (DCP). We find the optimal control of the associated DCP by incorporating the Legendre-Fenchel transform and a formal Hamilton-Jacobi-Bellman (HJB) equation. Then, we ``translate'' this optimal strategy to the QCP, of which we obtain an asymptotically optimal policy. Apart from theoretical results, we also examine the REINFORCE algorithm, a Reinforcement learning (RL) approach, for solving stochastic controls motivated by recent literature. We highlight the advantages and limitations of simulation from theoretical results and data-driven algorithms.
