基于状态抽象的时变到达率多类排队系统的最优接纳控制
Optimal Admission Control for Multiclass Queues with Time-Varying Arrival Rates via State Abstraction
摘要：
我们考虑了一个新的排队问题，决策者必须选择接受或拒绝随机到达的任务到一个没有缓冲区的队列中处理的$N$相同的服务器。每个任务都有一个价格和一个类，价格是一个正实数。每类任务具有不同的价格分布和服务率，并根据非齐次泊松过程到达。目标是决定接受哪些任务，以便在有限的时间内使处理的任务的总价格最大化。我们制定的问题作为一个离散时间马尔可夫决策过程（MDP）的混合状态空间。我们证明了最优价值函数具有特定的结构，这使得我们能够精确地求解混合MDP。此外，我们还证明了，随着时间步长的减少，离散时间的解决方案接近原来的连续时间问题的最优解。为了提高我们的方法对更多任务类的可扩展性，我们提出了一种基于状态抽象的近似方法。我们验证了我们的方法对合成数据，以及一个真正的金融欺诈数据集，这是激励应用这项工作。
英文摘要：
We consider a novel queuing problem where the decision-maker must choose to accept or reject randomly arriving tasks into a no buffer queue which are processed by $N$ identical servers. Each task has a price, which is a positive real number, and a class. Each class of task has a different price distribution and service rate, and arrives according to an inhomogenous Poisson process. The objective is to decide which tasks to accept so that the total price of tasks processed is maximised over a finite horizon. We formulate the problem as a discrete time Markov Decision Process (MDP) with a hybrid state space. We show that the optimal value function has a specific structure, which enables us to solve the hybrid MDP exactly. Moreover, we prove that as the time step is reduced, the discrete time solution approaches the optimal solution to the original continuous time problem. To improve the scalability of our approach to a greater number of task classes, we present an approximation based on state abstraction. We validate our approach on synthetic data, as well as a real financial fraud data set, which is the motivating application for this work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
