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

## TL;DR

This paper analyzes the stability and moment bounds of networks with utility-maximising service allocations, providing new results for both finite and infinite networks using Lyapunov methods and limit approaches.

## Contribution

It introduces stability and moment bounds for finite and infinite networks under utility-maximising policies, including cases where fluid limits are not applicable.

## Key findings

- Established stability for finite networks under weak utility assumptions.
- Derived steady-state moment bounds for infinite networks via finite approximations.
- Applied Lyapunov-Foster criteria to a broad class of queueing systems.

## 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.