Fork and Join Queueing Networks with Heavy Tails: Scaling Dimension and Throughput Limit

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.