Hidden Convexity in Queueing Models
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915605951545344 |
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| author | Chen, Xin Xin, Linwei Zhao, Minda |
| author_facet | Chen, Xin Xin, Linwei Zhao, Minda |
| contents | We study the joint control of arrival and service rates in queueing systems with the objective of minimizing long-run expected cost minus revenue. Although the objective function is non-convex, first-order methods have been empirically observed to converge to globally optimal solutions. This paper provides a theoretical foundation for this empirical phenomenon by characterizing the optimization landscape and identifying a hidden convexity: the problem admits a convex reformulation after an appropriate change of variables. Leveraging this hidden convexity, we establish the Polyak-Lojasiewicz-Kurdyka (PLK) condition for the original control problem, which excludes spurious local minima and ensures global convergence for first-order methods. Our analysis applies to a broad class of $GI/GI/1$ queueing models, including those with Gamma-distributed interarrival and service times. As a key ingredient in the proof, we establish a new convexity property of the expected queue length under a square-root transformation of the traffic intensity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hidden Convexity in Queueing Models Chen, Xin Xin, Linwei Zhao, Minda Optimization and Control Probability We study the joint control of arrival and service rates in queueing systems with the objective of minimizing long-run expected cost minus revenue. Although the objective function is non-convex, first-order methods have been empirically observed to converge to globally optimal solutions. This paper provides a theoretical foundation for this empirical phenomenon by characterizing the optimization landscape and identifying a hidden convexity: the problem admits a convex reformulation after an appropriate change of variables. Leveraging this hidden convexity, we establish the Polyak-Lojasiewicz-Kurdyka (PLK) condition for the original control problem, which excludes spurious local minima and ensures global convergence for first-order methods. Our analysis applies to a broad class of $GI/GI/1$ queueing models, including those with Gamma-distributed interarrival and service times. As a key ingredient in the proof, we establish a new convexity property of the expected queue length under a square-root transformation of the traffic intensity. |
| title | Hidden Convexity in Queueing Models |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2511.03955 |