L\'evy-driven queuing networks in multi-scale light and heavy traffic
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\'evy 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\'evy 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.
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