具有不可观测退缩行为的队列服务价值参数估计
Estimation of service value parameters for a queue with unobserved balking
AI总结：
本文研究了顾客服务价值差异的队列模型，通过最大似然估计法估计服务价值参数，并构建动态定价方案以最大化收益。
摘要：
在Naor模型中，顾客在观察队列长度后决定是否加入队列。本文考虑顾客在服务价值（奖励）R上异质，而在系统内停留成本上同质的情况。假设顾客价值为独立同分布的随机变量，管理者观察队列长度过程但不观察退缩顾客。假设R的分布具有已知参数形式，基于队列长度数据构造最大似然估计器以估计R的参数。提供验证条件以确保估计器的一致性和渐近正态性。进一步利用估计过程构建动态定价方案，通过迭代更新价格以估计收益最大化的准入价格。通过一系列模拟实验研究估计器和定价算法的性能。
英文摘要：
In Naor's model [17], customers decide whether or not to join a queue after observing its length. This work considers a variation in which customers are heterogeneous in their service value (reward) $R$ from completed service and homogeneous in the cost of staying in the system per unit of time. It is assumed that the values of customers are independent random variables generated from a common parametric distribution. The manager observes the queue length process, but not the balking customers. Assuming that the distribution of $R$ admits a known parametric form, a Maximum Likelihood Estimator based on the queue length data is constructed for the underlying parameters of $R$. We provide verifiable conditions for which the estimator is consistent and asymptotically normal. The estimation procedure is further leveraged to construct a dynamic pricing scheme that estimates the revenue maximizing admission price by iteratively updating the price using the estimated parameters. The performance of the estimator and the pricing algorithm are studied through a series of simulation experiments.
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