The age of gossip: Spatial mean-field regime
Disseminating a piece of information, or updates for a piece of information, has been shown to benefit greatly from simple randomized procedures, sometimes referred to as gossiping, or epidemic algorithms. Similarly, in a network where mobile nodes occasionally receive updated content from a base station, gossiping using opportunistic contacts allows for recent updates to be efficiently maintained, for a large number of nodes. In this case, however, gossiping depends on node mobility. For this reason, we introduce a new gossip model, with mobile nodes moving between different classes that can represent locations or states, which determine gossiping behavior of the nodes. Here we prove that, when the number of mobile nodes becomes large, the age of the latest updates received by mobile nodes approaches a deterministic mean-field regime. More precisely, we show that the occupancy measure of the process constructed, with the ages defined above, converges to a deterministic limit that can be entirely characterized by differential equations. This major simplification allows us to characterize how mobility, source inputs and gossiping influence the age distribution for low and high ages. It also leads to a scalable numerical evaluation of the performance of mobile update systems, which we validate (using a trace of 500 taxicabs) and use to propose infrastructure deployment.