在具有未知服务速率的$M/M/k/k+N$排队系统中学习最优接纳
Learning to Admit Optimally in an $M/M/k/k+N$ Queueing System with Unknown Service Rate
AI总结：
在具有未知服务速率的$M/M/k/k+N$排队系统中，通过参数学习方法设计最优调度策略以最大化长期平均奖励。
摘要：
受Erlang-B阻塞模型和扩展的$M/M/k/k+N$模型的启发，该模型允许某些排队，不仅限于通信网络，还应用于生产、消息和基于应用程序的停车系统中的容量和定价问题，我们研究了此类系统中具有未知服务速率的接入控制。在我们的模型中，调度器要么将每个到达的请求接纳进系统（当有空间时），要么将其阻塞。每个被服务的任务提供固定的奖励，但会带来每单位时间的持有成本，包括如果有的话在队列中等待服务的时间。我们的目标是设计一种调度策略，通过观察到达时间和系统状态，在到达时进行现实的决策事件驱动采样，以最大化长期平均奖励。调度器既不观察服务时间，也不观察离开时间点，这排除了使用基于奖励的强化学习方法。我们开发了我们的学习调度方案作为参数学习问题，类似于自适应控制中的自调节方法。在我们的问题中，确定性等价控制在有空间时总是接纳（无限次探索），并在没有空间时永不接纳（终止学习），因此在精心选择的时间点上避免永不接纳的建议。我们证明了我们提出的策略渐近收敛到最优策略，并提供了有限时间遗憾保证。控制策略之间的极端对比体现在我们针对不同参数情况的遗憾界中：一个情况是常数，另一个情况是对数。
英文摘要：
Motivated by applications of the Erlang-B blocking model and the extended $M/M/k/k+N$ model that allows for some queueing, beyond communication networks to sizing and pricing in production, messaging, and app-based parking systems, we study admission control for such systems with unknown service rate. In our model, a dispatcher either admits every arrival into the system (when there is room) or blocks it. Every served job yields a fixed reward but incurs a per unit time holding cost which includes the waiting time in the queue to get service if there is any. We aim to design a dispatching policy that maximizes the long-term average reward by observing arrival times and system state at arrivals, a realistic decision-event driven sampling of such systems. The dispatcher observes neither service times nor departure epochs, which excludes the use of reward-based reinforcement learning approaches. We develop our learning-based dispatch scheme as a parametric learning problem a'la self-tuning adaptive control. In our problem, certainty equivalent control switches between always admit if room (explore infinitely often), and never admit (terminate learning), so at judiciously chosen times we avoid the never admit recommendation. We prove that our proposed policy asymptotically converges to the optimal policy and present finite-time regret guarantees. The extreme contrast in the control policies shows up in our regret bounds for different parameter regimes: constant in one versus logarithmic in another.
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。
