{"ID":2845124,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.03955","arxiv_id":"2511.03955","title":"Hidden Convexity in Queueing Models","abstract":"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.","short_abstract":"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 theoretica...","url_abs":"https://arxiv.org/abs/2511.03955","url_pdf":"https://arxiv.org/pdf/2511.03955v2","authors":"[\"Xin Chen\",\"Linwei Xin\",\"Minda Zhao\"]","published":"2025-11-06T01:15:45Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}