Reduction of Subtask Dispersion in Fork-Join Systems

Fork-join and split-merge queueing systems are well-known abstractions of parallel systems in which each incoming task splits into subtasks that are processed by a set of parallel servers. A task exits the system when all of its subtasks have completed service. Two key metrics of interest in such systems are task response time and subtask dispersion. This paper presents a technique applicable to a class of fork-join systems with heterogeneous exponentially distributed service times that is able to reduce subtask dispersion with only a marginal increase in task response time. Achieving this is challenging since the unsynchronised operation of fork-join systems naturally militates against low subtask dispersion. Our approach builds on our earlier research examining subtask dispersion and response time in split-merge systems, and involves the frequent application and updating of delays to the subtasks at the head of the parallel service queues. Numerical results show the ability to reduce dispersion in fork-join systems to levels comparable with or below that observed in all varieties of split-merge systems while retaining the response time and throughput benefits of a fork-join system.