  Considering the widespread use of effective capacity in cross-layer design
and the extensive existence of renewal service processes in communication
networks, this paper thoroughly investigates the effective capacity for renewal
processes. Based on Z-transform, we derive exact analytical expressions for the
effective capacity at a given quality of service (QoS) exponent for both the
renewal processes with constant reward and with variable rewards. Unlike prior
literature that the effective capacity is approximated with no many insightful
discussions, our expression is simple and reveals further meaningful results,
such as the monotonicity and bounds of effective capacity. The analytical
results are then applied to evaluate the cross-layer throughput for diverse
hybrid automatic repeat request (HARQ) systems, including fixed-rate HARQ
(FR-HARQ, e.g., Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with
incremental redundancy (HARQ-IR)), variable-rate HARQ (VR-HARQ) and
cross-packet HARQ (XP-HARQ). Numerical results corroborate the analytical ones
and prove the superiority of our proposed approach. Furthermore, targeting at
maximizing the effective capacity via the optimal rate selection, it is
revealed that VR-HARQ and XP-HARQ attain almost the same performance, and both
of them perform better than FR-HARQ.
