In-Queue Priority Purchase

Abstract The extant priority-purchasing literature has restricted attention to the case where the only epoch for customers to purchase priority is upon arrival , and if customers choose not to upgrade when they arrive, they cannot do so later during their wait. A natural alternative is to let customers pay and upgrade to priority at any time during their stay in the queue, even if they choose not to do so initially. For instance, visitors to the London Eye could purchase a fast-track ticket at any point in their waiting process. Likewise, USCIS could allow a petitioner to file a request of expedited processing at any time after submission, not just at the moment of submission. If in-queue priority purchase is enabled, an immediate follow-up design question is whether to let customers in the regular line upgrade all at once (i.e., simultaneously ) or one at a time (i.e., sequentially ). In light of these considerations, this chapter examines the following two questions regarding in-queue priority purchase: (1) how will customers behave if they can upgrade to priority at any time during their wait in the queue? (2) how will rules on the specific timing of priority upgrade (i.e., simultaneous vs. sequential) impact customer behavior? This chapter is primarily based on Wang et al. (Queueing Syst 97:343–381, 2021) where interested readers can find proofs of the findings shown in this chapter.