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Priority queues are well understood in queueing theory. However, they are somewhat restrictive in that the low-priority customers suffer far greater waiting times than the highpriority customers. In this short paper, we introduce a novel generalization of a two-class priority queue, which we call Hybrid. We prove that Hybrid has a much broader achievability region than strict priority, allowing for a much greater range of waiting time pairs. We demonstrate settings where this new flexibility can increase the revenue obtained by a service system (like airport TSA) selling priority.
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When does partial priority improve revenue?
Abstract Priority queues have long been used to increase revenue by exploiting the fact that time-sensitive customers are willing to pay for shorter waiting times. This fact begs the question: Can one make even more revenue by relaxing the strictness of the priority policy? This paper answers this question under the unobservable queue setting, where customers are heterogeneous in their time-sensitivity; specifically the time-sensitivity of customers is allowed to follow an arbitrary distribution. In this paper, we prove necessary and sufficient conditions under which partial priority can increase the revenue. Specifically, we find a surprising result: Although partial priority offers much more flexibility than strict priority, partial priority only increases revenue if there are two additional constraints on the service provider, one setting a maximum price and the other setting a maximum waiting time. In the absence of either of these constraints, we prove that strict priority maximizes revenue. Finally, in situations where partial priority increases the revenue, we analytically characterize the amount of improvement.
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- PAR ID:
- 10675772
- Publisher / Repository:
- Queueing Systems
- Date Published:
- Journal Name:
- Queueing Systems
- Volume:
- 110
- Issue:
- 1
- ISSN:
- 0257-0130
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1007/s11134-025-09968-9
