Steady-State Analysis and Online Learning for Queues with Hawkes Arrivals

Xinyun Chen, Guiyu Hong
11/5/2023
math.PRcs.LGstat.ML

No confident code implementation found for this paper.

Abstract

We investigate the long-run behavior of single-server queues with Hawkes arrivals and general service distributions and related optimization problems. In detail, utilizing novel coupling techniques, we establish finite moment bounds for the stationary distribution of the workload and busy period processes. In addition, we are able to show that, those queueing processes converge exponentially fast to their stationary distribution. Based on these theoretic results, we develop an efficient numerical algorithm to solve the optimal staffing problem for the Hawkes queues in a data-driven manner. Numerical results indicate a sharp difference in staffing for Hawkes queues, compared to the classic GI/GI/1 model, especially in the heavy-traffic regime.

View on arXivView PDF

Code Implementations

No confident code match yet

We couldn't find an author-owned or strongly-evidenced community implementation for this paper. Any repos shown below are weak matches — verify before relying on them.

No code implementations found yet.

Know of an implementation? Let us know in the comments below!

Similar Papers

Analyzing homogenous and heterogeneous multi-server queues via neural networks

76% match2025

Online Learning and Optimization for Queues with Unknown Demand Curve and Service Distribution

76% match2023

Approximating G(t)/GI/1 queues with deep learning

76% match2024

Queueing-Aware Optimization of Reasoning Tokens for Accuracy-Latency Trade-offs in LLM Servers

75% match2026

Queueing Matching Bandits with Preference Feedback

75% match2026

Queue Scheduling with Adversarial Bandit Learning

74% match2023

Cite this paper

@article{chen2023steadystate,
  title  = {Steady-State Analysis and Online Learning for Queues with Hawkes Arrivals},
  author = {Xinyun Chen and Guiyu Hong},
  year   = {2023},
  eprint = {2311.02577},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2311.02577v2}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2311.02577.svg)](https://codeofpaper.com/paper/2311.02577)

Discussion