# On Maximizing the Probability of Achieving Deadlines in Communication Networks
## 9 Conclusions  
Maximizing the probability of achieving E2E communication delay deadlines in communication networks was studied. The deadline achievement probability for given routing tables was derived.  
We introduced a distributed iterative algorithm that finds the E2E delay cumulative probability functions. The algorithm was extended to also converge to optimal routing tables that maximized the probability for all packets to fulfill their deadlines. Both algorithms were proven to achieve a solution in a finite number of iterations. A solution was proposed that avoids the algorithms running into the \"count to infinity problem\".  
The simulation results show the proposed algorithms converging to the correct cumulative distribution functions of the deadline achievement probabilities for all nodes in a network.  
The deadline achievement ratio of the proposed algorithm with routing table optimization was benchmarked against the performance of routing by different common metrics (hop count, average delay, and ETX). The latter were tested, ruling out poor quality links using various thresholds for link packet loss ratios. It was shown that the proposed approach consistently outperformed the other routing metrics, regardless of the threshold used. Notably, the AMPAD exhibited an approximately 0.13 higher DAR performance compared with other approaches under intensive fading conditions (\(K=1\)).  
We further found that the proposed approach is versatile for coping with small-scale channel fading and varying traffic loads. Under strong fading conditions, our approach demonstrated a roughly 0.13 higher deadline achievement ratio compared with the benchmark protocols, with no significant performance improvement observed under mild fading conditions. Additionally, across varying traffic loads, our approach outperformed the benchmark protocols by up to 0.15.  
Deadline-aware routing using link statistics is a promising approach, especially for severe channel fading conditions.  
**Author Contributions:** Conceptualization, C.O., B.B. and T.M.; methodology, C.O. and B.B.; software, B.B.; validation, C.O., B.B. and T.M.; formal analysis, B.B.; investigation, C.O. and B.B.; resources, R.S., C.O., B.B. and T.M.; data curation, C.O. and B.B.; writing--original draft preparation, C.O. and B.B.; writing--review and editing, R.S., C.O., B.B. and T.M.; visualization, C.O. and B.B.; supervision, R.S. and T.M.; project administration, C.O. and T.M.; funding acquisition, R.S., C.O. and B.B. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported in Chile by the Research Center for Integrated Disaster Risk Management (CIGIDEN), Proyecto 1522A0005 FONDAP 2022, the German Research Foundation (DFG) within the Collaborative Research Center (CRC) 1053 MAKI, and the LOEWE initiative (Hessen, Germany) within the emergencITY center.  
**Data Availability Statement:** The software presented in this study is openly available in the GitHub code repository ([PERSON], Maximizing the Probability of Achieving Deadlines, 2024).  
**Conflicts of Interest:** The authors declare no conflict of interest.