Feedback, queueing, and the reliability of the ideal Poisson channel above capacity

The ideal Poisson channel, the ideal Poisson channel with feedback, the exponential-server timing channel, and the exponential-server timing channel with feedback are known to have the same capacity. We show that above this capacity they have the same reliability function, which we determine. For the ideal Poisson channel without feedback, this improves upon the strong converse of Burnashev and Kutoyants.