Optimizing queues with sunk cost fallacy

Abstract

We study an M/M/1 queue with customers subject to sunk cost fallacy caused by reference effect and loss aversion. The customers can purchase any quantity (even fractional) when they are in service. Also, the customers are assumed to be rational before joining the queueing system. However, once they join the queue, their purchasing quantity decisions can be affected by actual average waiting time. We fully characterize the purchasing decisions of customers with sunk cost fallacy in equilibrium, and it turns out that the decision is S-shaped in the actual waiting time and is increasing in the actual waiting time. We consider cases where customers may or may not observe the queue length information upon their arrivals. In the case of unobservable queue, we show that in the presence of sunk cost fallacy, the firm's profit is unimodal in service rate and waiting cost, which is different from that in a system without sunk cost fallacy. These facts imply that, the firm may not choose to speed up the service rate even though the it's costless to do so; moreover, the firm may not manage to improve the queueing experience in the unobservable case. We also show that a firm that ignores sunk cost fallacy while this phenomenon indeed exists may underprice or overprice the products, which may lead to a substantial loss. Similar findings are identified in the case of observable queue. Besides, we can conclude from our study that the higher degree of sunk cost fallacy, the higher profit the firm can gain. Last but not the least, disclosing the queue length information may not always benefit the firm.