Information in tweets: Analysis of a bufferless timing channel model

There has been a considerable interest in quantifying the influence that one node exerts on another in a social network. Using directed information, we study the problem for a simple, two-node network that models two users in a Twitter network in which one user (Alice) influences the other user (Bob) through her tweets. Under this setup, we relate the problem of direction of influence to the calculation of directed information from the input to the output in a bufferless single-server timing queue. Based on this relationship, we compute the directed information rate from Alice to Bob and, under simplifying assumptions, relate that rate to the distributions of Alice's tweet timings and Bob's action timings.