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1 results

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

  • Part of
  • Seva Shneer, Alexander Stolyar
  • Journal:
    Advances in Applied Probability / Volume 52 / Issue 2 / June 2020
    Published online by Cambridge University Press:
    15 July 2020, pp. 463-490
    Print publication:
    June 2020

  • 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.