This paper investigates the distribution of delay and peak age of information
in a communication system where packets, generated according to an independent
and identically distributed Bernoulli process, are placed in a single-server
queue with first-come first-served discipline and transmitted over an additive
white Gaussian noise (AWGN) channel. When a packet is correctly decoded, the
sender receives an instantaneous error-free positive acknowledgment, upon which
it removes the packet from the buffer. In the case of negative acknowledgment,
the packet is retransmitted. By leveraging finite-blocklength results for the
AWGN channel, we characterize the delay violation and the peak-age violation
probability without resorting to approximations based on large deviation theory
as in previous literature. Our analysis reveals that there exists an optimum
blocklength that minimizes the delay violation and the peak-age violation
probabilities. We also show that one can find two blocklength values that
result in very similar average delay but significantly different delay
violation probabilities. This highlights the importance of focusing on
violation probabilities rather than on averages.Comment: 5 pages, 5 figures, accepted for IEEE International Symposium on
Information Theory 2018, Edit: corrected peak-age of information formul
