Scheduling Parallel DAG Jobs Online

Transcription

1 Scheduing Parae DAG Jobs Onine Ben Moseey (CMU) Joint work with: Kuna Agrawa (WahsU) Jing Li (NJIT) Kefu Lu (WashU/CMU)

2 Cient-Server Scheduing Cients send parae jobs to the server Jobs schedue on identica processors/machines Server processes jobs and provides service guarantees Jobs arrive over time onine Jobs can be preempted Worst case setting 2

3 Service Guarantees Fow time difference between arriva and competion of a job Common objectives in onine scheduing: Average/Sum Fow Time Maximum Fow Time Throughput Time Arriva Job's Fow Time Competion 3

4 Paraeism Modes Speed-up Curves Jobs associated with speed-up functions Directed-Acycic Graph (DAG) Mode Jobs have work which correspond to a DAG Each job is modeed as a DAG Job competed when ast node of its DAG is competed Processing rate depends on the number of nodes being worked on 4

5 Paraeism Modes Speed-Up Curves Jobs have tota work W divided into phases Each phase has work Phases are processed sequentiay Processing rate function Γ(m) Function of number of processors given Function is usuay positive sub-inear Function can be different depending on the phase the job is currenty in. A Job's Phases 5

6 Directed Acycic Graph Mode of Paraeism Nodes represent computation Arrows represent dependencies 6

7 Onine Study of Modes DAG mode We-studied offine Ony studied recenty onine Naturay captures programs generated by anguages and ibraries such as Cik, Cik Pus, Inte TBB, OpenMP. Used by appied communities: Cyber-Physica-Systems (Rea-Time) community excited (Outstanding paper award ECTRS 2013, Best- Student-Paper Award RTSS 2011) 7

8 Resuts First resuts for average fow in DAG mode Average Fow Time [SODA 2016] LAPS is (1+ε) speed O(1) competitive, for fixed ε>0 Best theoreticay possibe Throughput [LATIN 2018] A (1+ε) speed O(1) competitive agorithm for fixed ε>0 Best theoreticay possibe Maximum Fow time [SPAA 2016] A (1+ε) speed O(1) competitive agorithm, for fixed ε>0 Open if speed is needed Agorithm is practica

9 Agortihm Deveopment DAG mode has been popuar because of its connection to practice We studied for scheduing a singe DAG job to minimize makespan Work steaing agorithm: good practica and theoretica performance Used in numerous systems for scheduing a parae job Non-cairvoyant Distributed protoco No preemption Want to emuate this success and use theory for FIFO to guide a modification of Work- Steaing

10 Work-Steaing Core 1 Core 2 Core 3 push pop doube ended queues Stea

11 Exampe: FIFO FIFO: Execute avaiabe nodes of job(s) with eariest arriva Coud be more than one job depending on ready nodes

12 FIFO: Impementation Chaenges Core 1 Core 2 Core 3 Job 1 time 0 Job 2 time 1

13 FIFO: Impementation Chaenges A goba queue Q storing a avaiabe nodes Core 1 Core 2 Job 1 time 0 Job 2 time 1 Core 3 Q Time

14 FIFO: Impementation Chaenges A goba queue Q storing a avaiabe nodes Job 1 time 0 Job 2 time 1 Core 1 Core 2 Core 3 Q Job s arriva time Time

15 FIFO: Impementation Chaenges A goba queue Q storing a avaiabe nodes Each core at each time step Job 1 time 0 executes one node in Q from the job with the eariest arriva time Job 2 time 1 Core 1 Core 2 Core 3 Q Job s arriva time Time

16 FIFO: Impementation Chaenges A goba queue Q storing a avaiabe nodes Each core at each time step Job 1 time 0 executes one node in Q from the job with the eariest arriva time Job 2 time 1 Core 1 Core 2 Core 3 Q Job s arriva time 1 0 Time

17 Work Steaing for Mutipe jobs Cores Parae jobs arrive at goba queue FIFO order C B admit 1 2 execute 3 stea (1) Each core has a queue and executes work from it (2) Ony when the oca queue runs out of work, a core wi admit a job from goba queue (3) Agorithm can stea for other queues or from the goba queue Has the same theoretica guarantees as FIFO and gave good practica performance

18 Concusion New resuts for scheduing DAG jobs onine Resuts have ead to practicay usabe agorithms for minimizing maximum fow time Recent resuts submitted for average fow time Much harder due to the need for preemptions Open Questions: Is resource augmentation needed for maximum fow time in the DAG and speed up curve mode (knowing paraeism)? Practica agorithm for throughput maximization?

19 Thank You! Questions? Max fow time (sec) Bing workoad OPT stea-k-first admit-first Max fow time (sec) OPT stea-k-first admit-first Finance workoad Max fow time (sec) OPT stea-k-first admit-first Log-norma workoad QPS QPS QPS (a) Bing workoad (b) Finance workoad (c) Log-norma workoad 19