Mobility in Age-Based Gossip Networks

TL;DR

It is shown that mobility can decrease the version age of nodes in a disconnected network from linear scaling in $n$ to at most square root scaling and even to constant scaling in some cases.

Abstract

We consider a gossiping network where a source forwards updates to a set of $n$ gossiping nodes that are placed in an arbitrary graph structure and gossip with their neighbors. In this paper, we analyze how mobility of nodes affects the freshness of nodes in the gossiping network. To model mobility, we let nodes randomly exchange positions with other nodes in the network. The position of the node determines how the node interacts with the rest of the network. In order to quantify information freshness, we use the version age of information metric. We use the stochastic hybrid system (SHS) framework to derive recursive equations to find the version age for a set of positions in the network in terms of the version ages of sets of positions that are one larger or of the same size. We use these recursive equations to find an upper bound for the average version age of a node in two example networks. We show that mobility can decrease the version age of nodes in a disconnected network from linear scaling in $n$ to at most square root scaling and even to constant scaling in some cases. We perform numerical simulations to analyze how mobility affects the version age of different positions in the network and also show that the upper bounds obtained for the example networks are tight.

Figures (9)

• Figure 1: A gossiping network where each node can gossip with its neighbors, denoted by black lines, and exchange positions with some nodes in the network, denoted by red arrows.
• Figure 2: An illustration of the mobility model in the gossiping network. The positions where node exchanges are possible are denoted by red arrows in the network on the top. As shown by the yellow arrows in the process, nodes $1$ and $3$ exchange positions, followed by nodes $2$ and $4$, and finally nodes $1$ and $2$ exchange positions.
• Figure 3: Toy example in yates21gossip, with mobility. Left: nodes in positions $1$ and $3$ can exchange positions. Right: nodes in positions $1$ and $2$ can exchange positions.
• Figure 4: A gossiping network where $\mathcal{N}_{FC}$ is a fully connected network of $6$ nodes $\{1, 2, 3, 4, 5, 6\}$ and $\mathcal{N}_{s}$, represented by position $7$, is a single node. Both parts receive updates as a rate $\frac{\lambda}{2}$ Poisson process from the source. Further, every node in $\mathcal{N}_{FC}$ can exchange positions with the node in $\mathcal{N}_{s}$, as shown by the red arrows.
• Figure 5: A disconnected gossiping network which has $6$ nodes, and nodes in two adjacent positions gossip with each other, but not with nodes in any other position, i.e., a node in each position can gossip with a node only in one other position. This is represented by solid black double-sided arrows. Further, a node in any position can exchange positions with nodes in any other position in the network. This is represented by red dashed arrows. $\{1,2\}$, $\{3,4\}$ and $\{5,6\}$ are adjacent node pairs. $\{1\}$ is a single node of the node pair $\{1,2\}$.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4