2025/03/20 by Nikolai Kriukov, Kriukov, Nikolai, Krzysztof Dȩbicki +3 · 1 citation
Business, Management and Accounting · Engineering · #Advanced Queuing Theory Analysis #Advanced Wireless Network Optimization #Reliability and Maintenance Optimization
paper · pdf · doi:10.48550/arxiv.2503.16633
We consider a queueing network operating under a strictly upper-triangular routing matrix with per column at most one non-negative entry. The root node is fed by a Gaussian process with stationary increments. Our aim is to characterize the distribution of the multivariate stationary workload process under a specific scaling of the queue's service rates. In the main results of this paper we identify, under mild conditions on the standard deviation function of the driving Gaussian process, in both light and heavy traffic parameterization, the limiting law of an appropriately scaled version (in both time and space) of the joint stationary workload process. In particular, we develop conditions under which specific queueing processes of the network effectively decouple, i.e., become independent in the limiting regime.