How Robust are Timely Gossip Networks to Jamming Attacks?

We consider a semantics-aware communication system, where timeliness is the semantic measure, with a source which maintains the most current version of a file, and a network of
$n$
user nodes with the goal to acquire the latest version of the file. The source gets updated with newer file versions as a point process, and forwards them to the user nodes, which further forward them to their neighbors using a memoryless gossip protocol. We study the average version age of the network in the presence of
$\tilde {n}$
jammers that disrupt inter-node communications, for the connectivity-constrained ring topology and the connectivity-rich fully connected topology. For the ring topology, we construct an alternate system model of mini-rings and prove that the version age of the original model can be sandwiched between constant multiples of the version age of the alternate model. We show in a ring network that when the number of jammers scales as a fractional power of the network size, i.e.,
$\tilde n= cn^{\alpha }$
, the version age scales as
$\sqrt {n}$
when
$\alpha < {}{}\frac {1}{2}$
, and as
$n^{\alpha }$
when
$\alpha \geq {}{}\frac {1}{2}$
. As the version age of a ring network without any jammers scales as
$\sqrt {n}$
, our result implies that the version age with gossiping is robust against up to
$\sqrt {n}$
jammers in a ring network. We then study the connectivity-rich fully connected topology, where we derive a greedy approach to place
$\tilde {n}$
jammers to maximize the age of the resultant network, which uses the jammers to isolate as many nodes as possible, thereby consolidating all links into a single mini-fully connected network. We show in this network that version age scales as
$\log {n}$
when
$\tilde {n}=cn\log {n}$
and as
$n^{\alpha -1}$
,
$1 < \alpha \leq 2$
when
$\tilde {n}=cn^{\alpha }$
, implying that the network is robust against
$n\log {n}$
jammers, since the age in a fully connected network without jammers scales as
$\log {n}$
. Finally, we present simulation results to support our theoretical findings.