Distributionally Robust Observable Strategic Queues

TL;DR

This paper extends Naor's analysis of join-or-balk in observable queues by incorporating distributional uncertainty, developing robust strategies under moment ambiguity and data-driven settings, and comparing outcomes with classical models.

Contribution

It introduces a distributionally robust framework for observable queues, deriving optimal strategies under uncertainty and extending classical results to data-driven scenarios.

Findings

Robust joining threshold strategies improve worst-case benefits.

Distributional ambiguity significantly impacts queue decision policies.

Comparison shows advantages over traditional sample average methods.

Abstract

This paper presents an extension of Naor's analysis on the join-or-balk problem in observable M/M/1 queues. While 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 perspective 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.