Foresee the Next Line: Customer Strategies and Information Disclosure in Tandem Queues
Ran Snitkovsky, Ricky Roet-Green, Jingwei Ji
Operations Research · 2026 · Volume 74 · Issue 2
Abstract
Many services consist of multiple stages, where each stage requires some waiting before completion. For example, customers who visit the Apple Store join the check-in queue first and then wait in another queue to be served by the Genius Bar technician. In such settings, customers often see the queue directly ahead of them but not the one in the next stage. Our paper aims to examine the impact of queue-length information on customers’ strategic behavior in such systems. We assume a two-stage tandem queueing system, with an admission queue followed by a treatment queue. Customers observe the queue length at arrival to each queue; they may balk or join and might later renege. We first study the fully observable model, in which queue-length information of both queues is available to customers at the time they arrive to the system. We calculate the equilibrium strategy and show that it depends on the number of customers in each queue and not necessarily on their mere sum. Next, we study the partially observable model, in which customers cannot observe the second queue length before completing service in the first one. Although this is the common practice, it is analytically more challenging. We prove the existence of a threshold equilibrium strategy in this model. It is shown in both models that customers who join the system never renege while waiting, yet in the partially observable model, they may balk when transitioning from one queue to another. To study the value of information, we compare the system performance in the fully and partially observable models. Combining extensive numeric calculations and exact analysis of a limiting parameter regime, we find that in general, the partially observable model yields higher throughput but lower social welfare compared with the fully observable model. Funding: This work was supported by the Shenzhen Research Institute of Big Data. This research was supported by the Jeremy Coller Foundation, the Henry Crown Institute of Business Research, and the Israeli Science Foundation [Grant 1361/23]. Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2023.0320 .
Keywords
Operations and Supply Chains, tandem queues, strategic queueing, queue-length information, reneging, throughput, social welfare
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