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

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  15 July 2020

Seva Shneer  and
Alexander Stolyar
Seva Shneer*
Affiliation:
Heriot-Watt University
Alexander Stolyar*
Affiliation:
University of Illinois
*
*Postal address: School of MACS, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom. Email: v.shneer@hw.ac.uk
**Postal address: ISE Department and Coordinated Science Lab, University of Illinois at Urbana-Champaign, Urbana, IL 61801. Email: stolyar@illinois.edu
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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.

Keywords

Stochastic stabilitystationary moment boundsutility-maximising service allocationsqueueing networkswireless networkssingle-hop networksmulti-hop networksinfinite networks

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M12: Network protocols
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 2 , June 2020 , pp. 463 - 490
Copyright
© Applied Probability Trust 2020

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