Fork-Join (FJ) queueing models capture the dynamics of system parallelization
under synchronization constraints, for example, for applications such as
MapReduce, multipath transmission and RAID systems. Arriving jobs are first
split into tasks and mapped to servers for execution, such that a job can only
leave the system when all of its tasks are executed.
In this paper, we provide computable stochastic bounds for the waiting and
response time distributions for heterogeneous FJ systems under general
parallelization benefit. Our main contribution is a generalized mathematical
framework for probabilistic server scheduling strategies that are essentially
characterized by a probability distribution over the number of utilized
servers, and the optimization thereof. We highlight the trade-off between the
scaling benefit due to parallelization and the FJ inherent synchronization
penalty. Further, we provide optimal scheduling strategies for arbitrary
scaling regimes that map to different levels of parallelization benefit. One
notable insight obtained from our results is that different applications with
varying parallelization benefits result in different optimal strategies.
Finally, we complement our analytical results by applying them to various
applications showing the optimality of the proposed scheduling strategies.Comment: 16 pages, 8 figure
