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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.11769 |
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| _version_ | 1866917986720284672 |
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| author | Dang, Yuchao Chi, Xuefen |
| author_facet | Dang, Yuchao Chi, Xuefen |
| contents | 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 $θ$, we propose a Micrometric Intervals based Supermartingale Upcrossing Estimate Theorem, quantifying the upper bound of event occurrence frequency to constrain the solution space of $θ$. 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 $θ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sliding Block Martingale based Multi-hop Delay QoS Analysis Dang, Yuchao Chi, Xuefen Information Theory 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 $θ$, we propose a Micrometric Intervals based Supermartingale Upcrossing Estimate Theorem, quantifying the upper bound of event occurrence frequency to constrain the solution space of $θ$. 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 $θ$ 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. |
| title | Sliding Block Martingale based Multi-hop Delay QoS Analysis |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.11769 |