L\'{e}vy-driven queuing networks in multi-scale light and heavy traffic
Probability
2026-02-05 v1
Abstract
We study a queueing network with a strictly upper-triangular routing matrix, where each column contains at most one non-negative entry, and the root node receives input from a spectrally positive L\'{e}vy process. Our aim is to characterize the distribution of the multivariate stationary workload under a specific scaling of the service rates. Under mild conditions on the Laplace exponent of the driving L\'{e}vy process, we identify the limiting law of an appropriately scaled joint stationary workload in both light-traffic and heavy-traffic regimes. In particular, we establish conditions under which certain queueing workloads within the network asymptotically decouple, becoming independent in the limiting regime.
Keywords
Cite
@article{arxiv.2602.04024,
title = {L\'{e}vy-driven queuing networks in multi-scale light and heavy traffic},
author = {Krzysztof Dȩbicki and Nikolai Kriukov and Michel Mandjes},
journal= {arXiv preprint arXiv:2602.04024},
year = {2026}
}