Transition time asymptotics of queue-based activation protocols in random-access networks

Sem Borst; Frank den Hollander; Francesca R. Nardi; Matteo Sfragara

doi:10.1016/j.spa.2020.08.004

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arXiv · 1807.05851

Transition time asymptotics of queue-based activation protocols in random-access networks

Sem Borst·Frank den Hollander·Francesca R. Nardi·Matteo Sfragara

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Abstract

We consider networks where each node represents a server with a queue. An active node deactivates at unit rate. An inactive node activates at a rate that depends on its queue length, provided none of its neighbors is active. For complete bipartite networks, in the limit as the queues become large, we compute the average transition time between the two states where one half of the network is active and the other half is inactive. We show that the law of the transition time divided by its mean exhibits a trichotomy, depending on the activation rate functions.

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Sem Borst, Frank den Hollander, Francesca R. Nardi, Matteo Sfragara. 2018-07-16. Transition time asymptotics of queue-based activation protocols in random-access networks. https://doi.org/10.1016/j.spa.2020.08.004

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