Non-Asymptotic Delay Bounds for (k,l) Fork-Join Systems and Multi-Stage Fork-Join Networks
Abstract
Parallel systems have received increasing attention with numerous recent applications such as fork-join systems, load-balancing, and l-out-of-k redundancy. Common to these systems is a join or resequencing stage, where tasks that have finished service may have to wait for the completion of other tasks so that they leave the system in a predefined order. These synchronization constraints make the analysis of parallel systems challenging and few explicit results are known. In this work, we model parallel systems using a max-plus approach that enables us to derive statistical bounds of waiting and sojourn times. Taking advantage of max-plus system theory, we also show end-to-end delay bounds for multi-stage fork-join networks. We contribute solutions for basic G|G|1 fork-join systems, parallel systems with load-balancing, as well as general (k,l) fork-join systems with redundancy. Our results provide insights into the respective advantages of l-out-of-k redundancy vs. load-balancing.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2015
- DOI:
- 10.48550/arXiv.1512.08354
- arXiv:
- arXiv:1512.08354
- Bibcode:
- 2015arXiv151208354F
- Keywords:
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- Computer Science - Performance;
- Computer Science - Networking and Internet Architecture