End-to-End Delay Analysis for Multi-hop Wireless Links Based on Martingale Theory

In this paper, we derive a new method based on the martingale theory to analyse the end-to-end (E2E) delay of multi-hop wireless links (MWL). First, the arrival-martingales and service-martingales are constructed in the signal-to-noise ratio (SNR) domain where fading channel characteristics are easily incorporated into the node's service. Then, a martingale parameter called the joint service descriptor is proposed to reflect the joint service capability of MWL for a specific arrival flow. Based on the above, we decouple the joint service and total delay threshold of MWL, which transforms the complex E2E delay analysis into the simple delay analysis of all single nodes. Finally, a closed-form expression for the E2E delay violation probability bounds is derived. Simulation results verify the accuracy and generality of our derived method in E2E delay analysis.