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}
}