A simple memoryless proof of the capacity of the exponential server timing channel

This paper provides a conceptually simple, memoryless-style proof to the capacity of the Anantharam and Verdu´s exponential server timing channel (ESTC). The approach is inspired by Rubin´s approach for characterizing the rate-distortion of a Poisson process with structured distortion measures. This approach obviates the need for using the information density to prove achievability, by exploiting: 1) the ESTC channel on [0, nT] law is a product of [0, T] ESTC channel laws given intermediate queue states; 2) for Poisson inputs, the queue states form a Harris-recurrent Markov process. Achievability is subsequently shown by first demonstrating via the law of large numbers for Markov chains that an AEP holds, followed by standard random coding arguments. We extend our methodology to demonstrate achievability with Poisson inputs for any point process channel where the conditional intensity at any time is only a function of the queue state. Lastly, we demonstrate achievability with Poisson inputs for the tandem queue.