Volume and Surface Dimensions for Infinite Networks

A Survey of Fractal Dimensions of Networks - SpringerBriefs in Computer Science ◽

10.1007/978-3-319-90047-6_7 ◽

2018 ◽

pp. 51-54

Author(s):

Eric Rosenberg

Keyword(s):

Infinite Networks

Download Full-text

Quasiharmonic classification of infinite networks

Discrete Applied Mathematics ◽

10.1016/0166-218x(80)90029-3 ◽

1980 ◽

Vol 2 (4) ◽

pp. 339-344 ◽

Cited By ~ 1

Author(s):

Maretsugu Yamasaki

Keyword(s):

Infinite Networks

Download Full-text

A relaxed small-gain theorem for discrete-time infinite networks

2020 59th IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc42340.2020.9303769 ◽

2020 ◽

Author(s):

Navid Noroozi ◽

Andrii Mironchenko ◽

Fabian R. Wirth

Keyword(s):

Discrete Time ◽

Small Gain Theorem ◽

Small Gain ◽

Infinite Networks

Download Full-text

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

Advances in Applied Probability ◽

10.1017/apr.2020.8 ◽

2020 ◽

Vol 52 (2) ◽

pp. 463-490

Author(s):

Seva Shneer ◽

Alexander Stolyar

Keyword(s):

Steady State ◽

Wide Class ◽

Continuous Time ◽

Service Rate ◽

Fluid Limit ◽

Natural Conditions ◽

Infinite Systems ◽

Moment Bounds ◽

Infinite Networks ◽

State Moment

AbstractWe 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.

Download Full-text