  Recently, hybrid-automatic-repeat-request (HARQ) systems have been favored in
particular state-of-the-art communications systems since they provide the
practicality of error detections and corrections aligned with repeat-requests
when needed at receivers. The queueing characteristics of these systems have
taken considerable focus since the current technology demands data
transmissions with a minimum delay provisioning. In this paper, we investigate
the effects of physical layer characteristics on data link layer performance in
a general class of HARQ systems. Constructing a state transition model that
combines queue activity at a transmitter and decoding efficiency at a receiver,
we identify the probability of clearing the queue at the transmitter and the
packet-loss probability at the receiver. We determine the effective capacity
that yields the maximum feasible data arrival rate at the queue under
quality-of-service constraints. In addition, we put forward non-asymptotic
backlog and delay bounds. Finally, regarding three different HARQ protocols,
namely Type-I HARQ, HARQ-chase combining (HARQ-CC) and HARQ-incremental
redundancy (HARQ-IR), we show the superiority of HARQ-IR in delay robustness
over the others. However, we further observe that the performance gap between
HARQ-CC and HARQ-IR is quite negligible in certain cases. The novelty of our
paper is a general cross-layer analysis of these systems, considering
encoding/decoding in the physical layer and delay aspects in the data-link
layer.
