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This paper investigates the distribution of delay and peak age of informationin a communication system where packets, generated according to an independentand identically distributed Bernoulli process, are placed in a single-serverqueue with first-come first-served discipline and transmitted over an additivewhite Gaussian noise (AWGN) channel. When a packet is correctly decoded, thesender receives an instantaneous error-free positive acknowledgment, upon whichit removes the packet from the buffer. In the case of negative acknowledgment,the packet is retransmitted. By leveraging finite-blocklength results for theAWGN channel, we characterize the delay violation and the peak-age violationprobability without resorting to approximations based on large deviation theoryas in previous literature. Our analysis reveals that there exists an optimumblocklength that minimizes the delay violation and the peak-age violationprobabilities. We also show that one can find two blocklength values thatresult in very similar average delay but significantly different delayviolation probabilities. This highlights the importance of focusing onviolation probabilities rather than on averages.

Delay and Peak-Age Violation Probability in Short-Packet Transmissions