Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Probability

arXiv:1812.01435 (math)
[Submitted on 4 Dec 2018 (v1), last revised 20 Aug 2019 (this version, v2)]

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

Authors:Seva Shneer, Alexander Stolyar
View PDF
Abstract:We study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For {\em 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 {\em 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.
Subjects: Probability (math.PR)
MSC classes: 60K25, 68M12
Cite as: arXiv:1812.01435 [math.PR]
  (or arXiv:1812.01435v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.01435

Submission history

From: Seva Shneer [view email]
[v1] Tue, 4 Dec 2018 14:26:18 UTC (23 KB)
[v2] Tue, 20 Aug 2019 11:03:47 UTC (52 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.PR
< prev   |   next >
new | recent | 2018-12
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)