Non-clairvoyant Scheduling of Batched Parallel Jobs to Minimize Mean Response Time

This paper presents a new scheduling algorithm RAD, and shows that RAD efficiently schedules batched parallel jobs on multiprocessors. An early result by Deng et al. shows that Dynamic Equi-partitioning is 4-competitive for mean response time when the number of jobs is not more than the number of processors. Then, in STOC 97, Edmonds et al. show that the mean response time obtained by Equi-partitioning is 2 + √ 3 ≈ 3.74 competitive for jobs with multiple phases of arbitrary nondecreasing and sublinear speedup functions. We consider more realistic DAG job model, and schedule them without any prior information of jobs. Our main result shows that, RAD is 3-competitive with respect to mean response time for any batched DAG jobs under arbitrary workload. To the best of our knowledge, RAD offers the best mean response time bound for the schedule of batched parallel jobs. Furthermore, we offer a general technique for the proof of the mean response time for batched parallel jobs. We apply this technique in the analysis of Equi-partitioning. By using a much simpler proof, we can achieve the same bound 2 + √ 3 as Edmonds et al. Moreover, their old analysis is restricted to the class of jobs with multiple phases of arbitrary nondecreasing and sublinear speedup functions, while our new result is applicable to arbitrary DAG jobs. Technical Report TR-07-02, Center for Advanced Information System, School of Computer Engineering, Nanyang Technological University, Singapore. The authors’ e-mail addresses are: {heyu0006, sunh0007, hsu}@ntu.edu.sg This research was supported in part by Singapore-MIT Alliance.