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S. Deng, H. Zhao, Z. Xiang, C. Zhang, R. Jiang, Y. Li, J. Yin, S. Dustdar, A. Zomaya:
"Dependent Function Embedding for Distributed Serverless Edge Computing";
IEEE Transactions on Parallel and Distributed Systems, Volume 33 (2022), Issue 10; S. 2346 - 2357.

Edge computing is booming as a promising paradigm to extend service provisioning from the centralized cloud to the network edge. Benefit from the development of serverless computing, an edge server can be configured as a carrier of limited serverless functions, in the way of deploying Docker runtime and Kubernetes engine. Meanwhile, an application generally takes the form of directed acyclic graphs (DAGs), where vertices represent dependent functions and edges represent data traffic. The status quo of minimizing the completion time (a.k.a. makespan) of the application motivates the study on optimal function placement. However, current approaches lose sight of proactively splitting and mapping the traffic to the logical data paths between the heterogeneous edge servers, which could affect the makespan significantly. To remedy that, we propose an algorithm, termed as Dependent Function Embedding (DPE), to get the optimal edge server for each function to execute and the moment it starts executing. DPE finds the best segmentation of each data traffic by exquisitely solving several infinity norm minimization problems. DPE is theoretically verified to achieve the global optimality. Extensive experiments on Alibaba cluster trace show that DPE significantly outperforms two baseline algorithms in makespan by 43.19% and 40.71%, respectively.

Edge computing, dependent function embedding, directed acyclic graph, function placement, task scheduling

http://dx.doi.org/10.1109/TPDS.2021.3137380