Statistical Delay Bounds for Automatic Repeat Request Protocols with Pipelining

The recent trend towards low-latency wireless communication requires a notion of non-ergodic capacity that deals with delays. Significant research in areas, such as effective capacity, delay-constrained capacity, and stochastic service curves, has contributed such results for relevant physical layer aspects, like fading processes, interference, and multiple antenna systems. Less attention has been paid to actual implementations of link layer automatic repeat request protocols. Instead, error-free transmission using instantaneous channel state information, simple stop-and-wait protocols, or instantaneous feedback are frequently assumed. In this work, we investigate protocols with pipelining that deal with packet errors under non-negligible round-trip-times. We define a stochastic service curve model of a general class of automatic repeat request protocols with pipelining and derive statistical waiting time and sojourn time bounds. We discover two regimes: under low to moderate load retransmissions cause the largest part of the sojourn time, whereas under high load the waiting time dominates the sojourn time. Generally, with increasing round-trip-time the basic cases of stop-and-wait protocols or instantaneous feedback neglect relevant effects and provide less accurate estimates.