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<p>In Naor’s model (Econometrica 37:15–24, 1969), 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) <i>R</i> 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 <i>R</i> admits a known parametric form, a Maximum Likelihood Estimator based on the queue length data is constructed for the underlying parameters of <i>R</i>. We provide verifiable conditions for which the estimator is consistent and asymptotically normal. The estimation procedure is further leveraged to construt 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.</p>

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Estimation of service value parameters for a queue with unobserved balking

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月17日

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  • Daniel Podorojnyi,
  • Liron Ravner

摘要

In Naor’s model (Econometrica 37:15–24, 1969), 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 construt 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.