# Effective Capacity for Renewal Service Processes with Applications to HARQ Systems

## TL;DR

This paper derives simple analytical expressions for the effective capacity of renewal processes, applies them to evaluate various HARQ systems, and demonstrates the superiority of variable-rate and cross-packet HARQ over fixed-rate schemes.

## Contribution

It provides exact, insightful formulas for effective capacity in renewal processes and applies these to analyze and compare different HARQ system performances.

## Key findings

- Analytical expressions reveal monotonicity and bounds of effective capacity.
- Numerical results confirm the accuracy of the derived formulas.
- VR-HARQ and XP-HARQ outperform FR-HARQ in effective capacity.

## Abstract

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.