Managing retrial queueing systems with boundedly rational customers

Abstract

Bounded rationality includes potential cognitive deficits that limit human rational behaviour. In this paper, we allow for estimation errors of their utility and consider bounded rationality in queueing models with retrials. Upon arrival, customers decide whether to join the system based on their perceived utility, and their choice behaviour is characterised by a logit choice model. For a revenue-seeking server and a social planner, we investigate corresponding optimal pricing strategies. We find that the revenue-optimal price is no longer socially efficient in general but depends on the retrial rate. There exists a threshold such that the socially optimal price is greater than the revenue-optimal one when the retrial rate is below this threshold; otherwise, the revenue-optimal price is greater. A larger bounded rationality widens the gap between social welfare under the revenue- and socially optimal prices. Furthermore, the server’s revenue may increase or first decrease and then increase with respect to customers’ rationality levels, and the server may find it beneficial to reveal waiting time information when customers’ rationality is high. Finally, failing to account for customers’ bounded rationality can lead a significant revenue loss for the server and the proportion of such a revenue loss is close to 1 as customers become fully boundedly rational.

Keywords:

• Queueing
• bounded rationality
• pricing strategy
• information disclosure
• retrials

Acknowledgements

The authors thank the Editor-in-Chief, an anonymous Associate Editor, and the anonymous referees for their very helpful and constructive comments, which have led to significant improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (71901024, 71871008), China Postdoctoral Science Foundation (2019M650494), the Emerging Interdisciplinary Project of CUFE (21XXJC010) and the Fundamental Research Funds for the Central Universities (FRF-TP-19-004A1, FRF-IDRY-19-017).