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

TL;DR

This paper analyzes the asymptotic behavior of transition times in queue-based activation protocols within bipartite networks, revealing a trichotomy in the distribution of scaled transition times as queues grow large.

Contribution

It provides the first detailed asymptotic analysis of transition times in queue-dependent activation protocols for bipartite networks, highlighting the impact of activation functions.

Findings

Derived explicit formulas for transition times in large-queue limits

Identified a trichotomy in the distribution of scaled transition times

Demonstrated how activation functions influence network dynamics

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.