Reduction of Subtask Dispersion in Fork-Join Systems

Abstract

Abstract. 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.

Analysis of Fork/Join and Related Queueing Systems

“…We next discuss the issue of subtask dispersion in SM and F/J queueing systems following the discussion in Tsimashenka and Knottenbelt [2013b]. Jobs of the TSM require a variable number of servers to be acquired concurrently according to the job class, and all servers are released together as discussed in Section 6.3.…”

“…This is especially an issue when subtasks have variable service times. The strategy proposed in Tsimashenka and Knottenbelt [2013b] is to reduce the mean response time of tasks while minimizing the dispersion of its subtasks by delaying the activation of certain subtasks that are at the head of the parallel service queues. More specifically,…”

“…The CDF for the dispersion, which is the time from the completion of the first to the K th F/J task (X (K) − X (1) ) is given in Tsimashenka and Knottenbelt [2013b] as…”

“…(8.4.4) Subtask dispersion: This is the difference in time between the completion of the last and first subtask of an F/J request, where we have adopted the terminology in Tsimashenka and Knottenbelt [2013b]; thus, each task consists of K subtasks in a K-way F/J queueing system.…”

Balancing disk access times in RAID5 disk arrays in degraded mode by conditionally prioritizing fork/join requests

“…We are interested by the mean response time of F/J requests: R F/J K and also the mean task dispersion: T disp K , the time from the completion of the first to the last task of an F/J request [12]. Reducing T disp K is a desirable from the viewpoint of reducing buffering space requirements, but the same goal is attained by reducing R F/J k , since T disp K is related to it as shown by simulation results presented in Section 3 indicates…”