2018/12/04 by Seva Shneer, Shneer, Seva, Alexander Stolyar +1
Business, Management and Accounting · Computer Science · #60K25 #68M12 #Advanced Queuing Theory Analysis #FOS: Mathematics #Mobile Ad Hoc Networks #Network Traffic and Congestion Control #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1812.01435
openalex publication_date 2018/12/04 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
We study networks of interacting queues governed by utility-maximising\nservice-rate allocations in both discrete and continuous time. For em finite\nnetworks we establish stability and some steady-state moment bounds under\nnatural conditions and rather weak assumptions on utility functions. These\nresults are obtained using direct applications of Lyapunov-Foster-type\ncriteria, and apply to a wide class of systems, including those for which fluid\nlimit-based approaches are not applicable.\n We then establish stability and some steady-state moment bounds for two\nclasses of em infinite networks, with single-hop and multi-hop message\nroutes. These results are proved by considering the infinite systems as limits\nof their truncated finite versions. The uniform moment bounds for the finite\nnetworks play a key role in these limit transitions.\n