{"title":"Fork and Join Queueing Networks with Heavy Tails: Scaling Dimension and Throughput Limit","authors":"Yun Zeng, Jian Tan, Cathy H. Xia","doi":"10.1145/3219617.3219668","DOIUrl":null,"url":null,"abstract":"Parallel and distributed computing systems are foundational to the success of cloud computing and big data analytics. Fork-Join Queueing Networks with Blocking (FJQN/Bs) are natural models for such systems. While engineering solutions have long been made to build and scale such systems, it is challenging to rigorously characterize the throughput performance of ever-growing systems, especially in the presence of heavy-tailed delays. In this paper, we utilize an infinite sequence of FJQN/Bs to study the throughput limit and focus on regularly varying service times with index α>1. We introduce two novel geometric concepts - scaling dimension and extended metric dimension - and show that an infinite sequence of FJQN/Bs is throughput scalable if the extended metric dimension <α-1 and only if the scaling dimension łe α-1. These results provide new insights on the scalability of a rich class of FJQN/Bs.","PeriodicalId":210440,"journal":{"name":"Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3219617.3219668","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
Parallel and distributed computing systems are foundational to the success of cloud computing and big data analytics. Fork-Join Queueing Networks with Blocking (FJQN/Bs) are natural models for such systems. While engineering solutions have long been made to build and scale such systems, it is challenging to rigorously characterize the throughput performance of ever-growing systems, especially in the presence of heavy-tailed delays. In this paper, we utilize an infinite sequence of FJQN/Bs to study the throughput limit and focus on regularly varying service times with index α>1. We introduce two novel geometric concepts - scaling dimension and extended metric dimension - and show that an infinite sequence of FJQN/Bs is throughput scalable if the extended metric dimension <α-1 and only if the scaling dimension łe α-1. These results provide new insights on the scalability of a rich class of FJQN/Bs.