Wireless random‐access networks with bipartite interference graphs

Author:

Borst Sem C.1,den Hollander Frank2,Nardi Francesca R.13,Sfragara Matteo24

Affiliation:

1. Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven The Netherlands

2. Mathematical Institute Leiden University Leiden The Netherlands

3. Department of Mathematics University of Florence Florence Italy

4. Department of Mathematics Stockholm University Stockholm Sweden

Abstract

AbstractWe consider random‐access networks where nodes represent servers with a queue and can be either active or inactive. A node deactivates at unit rate, while it activates at a rate that depends on its queue length, provided none of its neighbors is active. We consider arbitrary bipartite graphs in the limit as the initial queue lengths become large and identify the transition time between the two states where one half of the network is active and the other half is inactive. The transition path is decomposed into a succession of transitions on complete bipartite subgraphs. We formulate a randomized greedy algorithm that takes the graph as input and gives as output the set of transition paths the network is most likely to follow. Along each path we determine the mean transition time and its law on the scale of its mean. Depending on the activation rates, we identify three regimes of behavior.

Publisher

Wiley

Subject

Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software

Reference4 articles.

1. Transition time asymptotics of queue‐based activation protocols in random‐access networks;Borst S. C.;Stoch. Process. Appl.,2020

2. Crossover times in bipartite networks with activity constraints and time‐varying switching rates;Borst S. C.;Ann. Appl. Probab,2022

3. Asymptotically exponential hitting times and metastability: A pathwise approach without reversibility;Fernandez R.;Electron. J. Probab.,2015

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