A short note on the monotonicity of the Erlang C formula in the Halfin-Whitt regime
Bernardo D'Auria
TL;DR
This paper proves a monotonicity property of the Erlang C formula in the Halfin-Whitt regime, confirming a recent conjecture and contributing to the theoretical understanding of queueing systems.
Contribution
It establishes a proven monotonicity condition for the Erlang C formula in the Halfin-Whitt regime, addressing a conjecture from prior research.
Findings
Erlang C formula satisfies a specific monotonicity condition in the Halfin-Whitt regime
The proven property confirms a recent conjecture in queueing theory
Enhances theoretical understanding of system performance in heavy-traffic regimes
Abstract
We prove a monotonicity condition satisfied by the Erlang C formula when computed in the Halfin-Whitt regime. This property was recently conjectured in Janssen et al. [2011].
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · Mathematical functions and polynomials · Holomorphic and Operator Theory