Abstract
This paper presents an extension of Naor’s analysis on the join-or-balk problem in observable M/M/1 queues. Although all other Markovian assumptions still hold, we explore this problem assuming uncertain arrival rates under the distributionally robust settings. We first study the problem with the classical moment ambiguity set, where the support, mean, and mean-absolute deviation of the underlying distribution are known. Next, we extend the model to the data-driven setting, where decision makers only have access to a finite set of samples. We develop three optimal joining threshold strategies from the perspectives of an individual customer, a social optimizer, and a revenue maximizer such that their respective worst-case expected benefit rates are maximized. Finally, we compare our findings with Naor’s original results and the traditional sample average approximation scheme.
Original language | English (US) |
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Pages (from-to) | 337-361 |
Number of pages | 25 |
Journal | Stochastic Systems |
Volume | 14 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2024 |
Externally published | Yes |
Keywords
- Naor’s model
- distributionally robust optimization
- economic queues
- parameter uncertainty
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Management Science and Operations Research