具有检查成本的队列：查看还是不查看？
Queues with inspection cost: To see or not to see?
AI总结：
本文研究带检查成本的 M/M/1 队列加入决策，给出均衡概率闭式解，并证明降低检查成本比提高加入奖励更能提升社会福利。
摘要：
考虑一个 M/M/1 型队列，加入队列可获得已知奖励，但排队期间每单位时间都要支付已知等待成本。20世纪60年代，Naor 证明，任何到达者在队列长度小于已知阈值时，加入队列都是最优的。然而，获取队列长度信息通常会带来额外成本，例如网站加载时间或数据漫游费用。因此，我们的模型为每个到达者提供三种选择：盲目加入、盲目离开，或支付已知检查成本，通过将队列长度与 Naor 阈值进行比较来作出最优加入决策。在最近一篇论文中，Hassin 和 Roet-Green 证明唯一 Nash 均衡始终存在，并划分了均衡概率非零的区域。我们通过在大多数情形下给出均衡概率的新闭式表达式来补充这些结果。此外，Hassin 和 Roet-Green 表明，最小化检查成本可使社会福利最大化。设想队列运营者选择投资方向，我们比较了降低检查成本与提高加入队列奖励对社会福利的影响。我们证明前者占优，而后者甚至可能对社会福利产生不利影响。
英文摘要：
Consider an M/M/1-type queue where joining attains a known reward, but a known waiting cost is paid per time unit spent queueing. In the 1960s, Naor showed that any arrival optimally joins the queue if its length is less than a known threshold. Yet acquiring knowledge of the queue length often brings an additional cost, e.g., website loading time or data roaming charge. Therefore, our model presents any arrival with three options: join blindly, balk blindly, or pay a known inspection cost to make the optimal joining decision by comparing the queue length to Naor's threshold. In a recent paper, Hassin and Roet-Green prove that a unique Nash equilibrium always exists and classify regions where the equilibrium probabilities are non-zero. We complement these findings with new closed-form expressions for the equilibrium probabilities in the majority of cases. Further, Hassin and Roet-Green show that minimizing inspection cost maximises social welfare. Envisaging a queue operator choosing where to invest, we compare the effects of lowering inspection cost and increasing the queue-joining reward on social welfare. We prove that the former dominates and that the latter can even have a detrimental effect on social welfare.
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。
