New resource augmentation analysis of the total stretch of SRPT and SJF in multiprocessor scheduling

This paper studies online job scheduling on multiprocessors and, in particular, investigates the algorithms SRPT and SJF for minimizing total stretch, where the stretch of a job is its flow time (response time) divided by its processing time. SRPT is perhaps the most well-studied algorithm for minimizing total flow time or stretch. This paper gives the first resource augmentation analysis of the total stretch of SRPT, showing that it is indeed O(1)-speed 1-competitive. This paper also gives a simple lower bound result that SRPT is not s-speed 1-competitive for any s 1). We conjecture that SRPT also admits a similar result.

[1]  Sanjeev Khanna,et al.  Algorithms for minimizing weighted flow time , 2001, STOC '01.

[2]  Luca Becchetti,et al.  Scheduling to minimize average stretch without migration , 2000, SODA '00.

[3]  Kirk Pruhs,et al.  Online weighted flow time and deadline scheduling , 2006, J. Discrete Algorithms.

[4]  Eric Torng,et al.  Applying extra-resource analysis to load balancing , 2000, SODA '00.

[5]  Jeff Edmonds,et al.  Scheduling in the dark , 1999, STOC '99.

[6]  Tak Wah Lam,et al.  Non-migratory online deadline scheduling on multiprocessors , 2004, SODA '04.

[7]  Prudence W. H. Wong,et al.  A unified analysis of hot video schedulers , 2002, STOC '02.

[8]  Nodari Vakhania,et al.  Preemptive scheduling in overloaded systems , 2003, J. Comput. Syst. Sci..

[9]  Bala Kalyanasundaram,et al.  Maximizing job completions online , 1998, J. Algorithms.

[10]  Rajmohan Rajaraman,et al.  Improved algorithms for stretch scheduling , 2002, SODA '02.

[11]  Yossi Azar,et al.  Minimizing Total Flow Time and Total Completion Time with Immediate Dispatching , 2003, SPAA '03.

[12]  Kirk Pruhs,et al.  Server scheduling in the Lp norm: a rising tide lifts all boat , 2003, STOC '03.

[13]  Cynthia A. Phillips,et al.  Optimal Time-Critical Scheduling via Resource Augmentation (Extended Abstract) , 1997, Symposium on the Theory of Computing.

[14]  Rajmohan Rajaraman,et al.  Online Scheduling to Minimize Average Stretch , 2004, SIAM J. Comput..

[15]  Stefano Leonardi,et al.  Approximating total flow time on parallel machines , 1997, STOC '97.

[16]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[17]  A. J. Clewett,et al.  Introduction to sequencing and scheduling , 1974 .

[18]  Ashish Goel,et al.  Multi-processor scheduling to minimize flow time with ε resource augmentation , 2004, STOC '04.

[19]  Michael A. Bender,et al.  Flow and stretch metrics for scheduling continuous job streams , 1998, SODA '98.

[20]  Kirk Pruhs,et al.  Online scheduling , 2003 .

[21]  Eric Torng,et al.  SRPT optimally utilizes faster machines to minimize flow time , 2004, SODA '04.