Problem definition: We develop a model to optimize the frequency of wait time updates for customers in an unobservable queue. Rather than assuming a predefined cost function for waiting, the model incorporates cognitive biases — loss aversion and discomfort with uncertainty - to quantify customer disutility during the wait. Embedded in an M/G/1 queueing framework, the model evaluates a class of information policies where a customer's expected wait time is revealed upon arrival and then updates are delivered periodically during the wait, i.e., every m service completions.
Methodology/results: We find that for purely loss-averse customers, sharing information only upon arrival (m=+\infty) is optimal, while sharing all information (m=1) is optimal for customers who focus on uncertainty. For customers who experience both sources of disutility, the paper derives a tractable approximation for highly-utilized systems. Analysis of the approximation finds that as system utilization or service-time variability increases, it is optimal to increase m and reduce the update frequency. We also show that a policy that does not reveal any information, and in particular does not even reveal expected wait time upon arrival, is never optimal. Numerical experiments confirm the robustness of the approximation and sensitivity analysis, even when server utilization is moderate.
Managerial implications: While waiting for service, customers can feel both frustration because of dashed expectations and anxiety due to uncertainty. A firm may ameliorate these emotions by updating the customer with information about the remaining wait. We find that both too much, and too little information can be damaging, and we derive a simple formula for the optimal rate of updating. In general, this work contributes a behavioral optimization framework to the queueing literature and offers practical insights for service providers aiming to enhance the customer experience through information sharing.
Keywords: Service Operations, Behavioral Operations, Queueing Theory, Stochastic Methods
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