Optimal Routing in Gossip Networks

In this paper, we introduce the Gossip Network model where travelers can obtain information about the state of dynamic networks by gossiping with peer travelers using ad hoc communication. Travelers then use the gossip information to recourse their path and find the shortest path to their destination. We study optimal routing in stochastic, time-independent gossip networks, and demonstrate that an optimal routing policy may direct travelers to make detours to gather information. A dynamic programming equation that produces the optimal policy for routing in gossip networks is presented. In general, the dynamic programming algorithm is intractable; however, for two special cases a polynomial optimal solution is presented. We show that ordinarily gossiping helps travelers decrease their expected path cost. However, in some scenarios, depending on the network parameters, gossiping could increase the expected path cost. The parameters that determine the effect of gossiping on the path costs are identified and their influence is analyzed. This dependency is fairly complex and was confirmed numerically on grid networks.