Scheduling Parallelizable Jobs Online to Minimize the Maximum Flow Time

Abstract

In this paper we study the problem of scheduling a set of dynamic multithreaded jobs with the objective of minimizing the maximum latency experienced by any job. We assume that jobs arrive online and the scheduler has no information about the arrival rate, arrival time or work distribution of the jobs. The scheduling goal is to minimize the maximum amount of time between the arrival of a job and its completion-this goal is referred to in scheduling literature as maximum flow time. While theoretical online scheduling of parallel jobs has been studied extensively, most prior work has focussed on a highly stylized model of parallel jobs called the "speedup curves model." We model parallel jobs as directed acyclic graphs, which is a more realistic way to model dynamic multithreaded jobs. In this context, we prove that a simple First-In-First-Out scheduler is (1 +)-speed O(1)-competitive for any > 0. We then develop a more practical work-stealing scheduler and show that it has a maximum flow time of O(1 2 max{OPT, ln(n)}) for n jobs, with (1 +)-speed. This result is essentially tight as we also provide a lower bound of Ω(log(n)) for work stealing. In addition, for the case where jobs have weights (typically representing priorities) and the objective is minimizing the maximum weighted flow time, we show a non-clairvoyant algorithm is (1 +)-speed O(1 2)-competitive for any > 0, which is essentially the best positive result that can be shown in the online setting for the weighted case due to strong lower bounds without resource augmentation. After establishing theoretical results, we perform an empirical study of work-stealing. Our results indicate that, on both real world and synthetic workloads, work-stealing performs almost as well as an optimal scheduler.

heSRPT: Parallel scheduling to minimize mean slowdown

“…The SPAA/parallel community has studied the problem of allocating servers to jobs which follow arbitrary speedup functions in order to minimize flow time [24,17,18,3]. Like our paper, [24] considers jobs of known size while [17,18,3] consider jobs of unknown size. These papers use competitive analysis, which assumes that job sizes, arrival times, and even speedup functions are adversarially chosen.…”

Towards Optimality in Parallel Job Scheduling

“…However, this has been through the lens of competitive analysis, which assumes the job sizes (service times), arrival times, and even speedup curves are adversarially chosen, e.g. [2,11,12]. Competitive analysis also does not yield closed form expressions for mean response time.…”

Speed Scaling with Multiple Servers Under A Sum Power Constraint

“…Prior Work The sub-linear-sched problem has been an object of immense interest [3,4,11,7,8,1], where practical algorithms include packing based [18], and resource reservation algorithms [14]. Heuristic policies with only numerical performance analysis can be found in [13].…”

“…Heuristic policies with only numerical performance analysis can be found in [13]. In past, this problem has been considered for the combinatorial discrete allocation model [11], where an integer number of servers are assigned to any job, as well as the continuous allocation model [7,8,1,3,4], that treats the N servers as a single resource block which can be partitioned into any size and assigned to any job.…”

“…For the discrete allocation model, in [11], a variant of the SRPT algorithm is shown to be 4 1/(1−1/α) log W competitive, where W = wmax/wmin is the ratio of the largest and the smallest job size. For the continuous allocation model, this problem has been considered in [7,8,1,3,4], where with resource augmentation, i.e., the online algorithm is allowed more resources, e.g., faster machines, than the OPT, algorithms with constant competitive ratios have been derived as a function of the resource augmentation factor.…”