English

Polling on a circle with non-uniform batch arrivals

Probability 2025-03-07 v1

Abstract

In this paper, we analyze a polling system on a circle with. Random batches of customers arrive at a circle, where each customer, independently, obtains a location according to a general distribution. A single server cyclically travels over the circle to serve all customers. We analyze the experienced delay of batches for two service policies: globally gated and exhaustive. The Laplace-Stieltjes transform of the experienced delay is found under the former policy. For the latter policy, we propose a mean-value analysis, resulting in an algorithmic approach for the evaluation of the mean experienced delay. Light- and heavy-traffic limits are derived exactly for the system performance.

Keywords

Cite

@article{arxiv.2503.04448,
  title  = {Polling on a circle with non-uniform batch arrivals},
  author = {Tim Engels and Ivo Adan and Onno Boxma and Jacques Resing},
  journal= {arXiv preprint arXiv:2503.04448},
  year   = {2025}
}
R2 v1 2026-06-28T22:09:14.222Z