Sliding Block Martingale based Multi-hop Delay QoS Analysis

Abstract

With the growing density of wireless networks and demand for multi-hop transmissions, precise delay Quality of Service (QoS) analysis has become a critical challenge. This paper introduces a multi-hop delay QoS analysis framework based on the sliding block martingale, addressing the loose boundary issue of prior methods that rely on service process martingales and min-plus transformations. By constructing a sliding block martingale with a window, we capture both long-term trends and short-term fluctuations in the backlog, eliminating the reliance on the generalized incremental property. The framework redefines delay unreliability events using cascading attributes, deriving a more compact Delay Unreliability Probability Boundary (DUPB). To improve the efficiency of solving the key parameter $\theta$, we propose a Micrometric Intervals based Supermartingale Upcrossing Estimate Theorem, quantifying the upper bound of event occurrence frequency to constrain the solution space of $\theta$. Simulations based on the 3GPP UMa/UMi channel model validate the framework's effectiveness. Results show that in 2-7 hop scenarios, the maximum deviation between theoretical boundaries and Monte Carlo simulations is $4.116 \times 10^{-5}$, with a lower RMSE than existing methods. Iteration count and CPU time for solving $\theta$ are reduced by $59\%-72\%$ and $60.6\%-70.5\%$, respectively, improving analysis efficiency. Furthermore, the derived minimum service rate for multi-hop queues offers a valuable reference for resource allocation. The framework demonstrates high accuracy, scalability, and practicality in complex multi-hop networks.