Optimal control for epidemic routing of two files with different priorities in Delay Tolerant Networks

We consider the problem of joint dissemination of multiple contents with different priorities through epidemic routing in a large Delay Tolerant Network (DTN). Specifically, we consider two files a and b to be distributed in a large capacity-limited DTN through opportunistic contacts between the roaming nodes. The goal is to maximize the number of nodes that receive the files within a delay window, but with a priority for file b over file a. This preference can reflect difference in popularity or significance of files, or offering different grades of service. The restriction is the short duration of encounters and limited transmission capacity of nodes, where decisions have to be made on which file to forward upon an opportunity of communication. By formulating this problem as an optimal control problem based on ordinary differential equations and analyzing it through Pontryagin´s Minimum Principle, we find that the optimal routing policies follow a simple but a priori counter-intuitive “bang-singular-bang” structure. Through numerical evaluations, we illustrate our findings and provide some intuitions about how the structure of the optimal policy changes with respect to different network settings.