Choosing Outdated Information to Achieve Reliability in Age-Based Gossiping

We consider a system model with two sources, a reliable source and an unreliable source, who are responsible for disseminating updates regarding a process to an age-based gossip network of
$n$
nodes. Nodes wish to have fresh information, however, they have preference for packets that originated at the reliable source and are willing to sacrifice their version age of information by up to
$G$
versions to switch from an unreliable packet to a reliable packet. We study how this protocol impacts the prevalence of unreliable packets at nodes in the network and their version age. Using a stochastic hybrid system (SHS) framework, we formulate analytical equations to characterize two quantities: expected fraction of nodes with unreliable packets and expected version age of information at network nodes. We show that as
$G$
increases, fewer nodes have unreliable packet, however, their version age increases as well, thereby inducing a freshness-reliability trade-off in the network. We present numerical results to support our findings.