Stability and moment bounds under utility-maximising service allocations: finite and infinite networks

Vsevolod Shneer, Alexander Stolyar

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Abstract

We study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For finite networks we establish stability and some steady-state moment bounds under natural conditions and rather weak assumptions on utility functions. These results are obtained using direct applications of Lyapunov–Foster-type criteria, and apply to a wide class of systems, including those for which fluid-limit-based approaches are not applicable. We then establish stability and some steady-state moment bounds for two classes of infinite networks, with single-hop and multi-hop message routes. These results are proved by considering the infinite systems as limits of their truncated finite versions. The uniform moment bounds for the finite networks play a key role in these limit transitions.
Original languageEnglish
Pages (from-to)463-490
Number of pages28
JournalAdvances in Applied Probability
Volume52
Issue number2
DOIs
Publication statusPublished - 15 Jul 2020

Keywords

  • Stochastic stability
  • infinite networks
  • multi-hop networks
  • queueing networks
  • single-hop networks
  • stationary moment bounds
  • utility-maximising service allocations
  • wireless networks

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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