### Abstract

We consider the classical problem of online job scheduling on uniprocessor and multiprocessor machines. For a given job, we measure the quality of service provided by an algorithm by the stretch of the job, which is defined as the ratio of the amount of time that the job spends in the system to the processing time of the job. For a given sequence of jobs, we measure the performance of an algorithm by the average stretch achieved by the algorithm over all the jobs in the sequence. The average stretch metric has been used to evaluate the performance of scheduling algorithms in many applications arising in databases, networks and systems; however, no formal analysis of scheduling algorithms is known for the average stretch metric. The main contribution of this paper is to show that the shortest remaining processing time algorithm (SRPT) is O(1)-competitive with respect to average stretch for both uniprocessors as well as multiprocessors. For uniprocessors, we prove that SRPT is 2-competitive; we also establish an essentially matching lower bound on the competitive ratio of SRPT. For multiprocessors, we show that the competitive ratio of SRPT is at most 14. Furthermore, we establish constant-factor lower bounds on the competitive ratio of any on-line algorithm for both uniprocessors and multiprocessors.

Original language | English (US) |
---|---|

Pages (from-to) | 433-443 |

Number of pages | 11 |

Journal | Annual Symposium on Foundations of Computer Science - Proceedings |

State | Published - Dec 1 1999 |

Event | Proceedings of the 1999 IEEE 40th Annual Conference on Foundations of Computer Science - New York, NY, USA Duration: Oct 17 1999 → Oct 19 1999 |

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### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science - Proceedings*, 433-443.

**Online scheduling to minimize average stretch.** / Muthukrishnan, Shanmugavelayutham; Rajaraman, Rajmohan; Shaheen, Anthony; Gehrke, Johannes E.

Research output: Contribution to journal › Conference article

*Annual Symposium on Foundations of Computer Science - Proceedings*, pp. 433-443.

}

TY - JOUR

T1 - Online scheduling to minimize average stretch

AU - Muthukrishnan, Shanmugavelayutham

AU - Rajaraman, Rajmohan

AU - Shaheen, Anthony

AU - Gehrke, Johannes E.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - We consider the classical problem of online job scheduling on uniprocessor and multiprocessor machines. For a given job, we measure the quality of service provided by an algorithm by the stretch of the job, which is defined as the ratio of the amount of time that the job spends in the system to the processing time of the job. For a given sequence of jobs, we measure the performance of an algorithm by the average stretch achieved by the algorithm over all the jobs in the sequence. The average stretch metric has been used to evaluate the performance of scheduling algorithms in many applications arising in databases, networks and systems; however, no formal analysis of scheduling algorithms is known for the average stretch metric. The main contribution of this paper is to show that the shortest remaining processing time algorithm (SRPT) is O(1)-competitive with respect to average stretch for both uniprocessors as well as multiprocessors. For uniprocessors, we prove that SRPT is 2-competitive; we also establish an essentially matching lower bound on the competitive ratio of SRPT. For multiprocessors, we show that the competitive ratio of SRPT is at most 14. Furthermore, we establish constant-factor lower bounds on the competitive ratio of any on-line algorithm for both uniprocessors and multiprocessors.

AB - We consider the classical problem of online job scheduling on uniprocessor and multiprocessor machines. For a given job, we measure the quality of service provided by an algorithm by the stretch of the job, which is defined as the ratio of the amount of time that the job spends in the system to the processing time of the job. For a given sequence of jobs, we measure the performance of an algorithm by the average stretch achieved by the algorithm over all the jobs in the sequence. The average stretch metric has been used to evaluate the performance of scheduling algorithms in many applications arising in databases, networks and systems; however, no formal analysis of scheduling algorithms is known for the average stretch metric. The main contribution of this paper is to show that the shortest remaining processing time algorithm (SRPT) is O(1)-competitive with respect to average stretch for both uniprocessors as well as multiprocessors. For uniprocessors, we prove that SRPT is 2-competitive; we also establish an essentially matching lower bound on the competitive ratio of SRPT. For multiprocessors, we show that the competitive ratio of SRPT is at most 14. Furthermore, we establish constant-factor lower bounds on the competitive ratio of any on-line algorithm for both uniprocessors and multiprocessors.

UR - http://www.scopus.com/inward/record.url?scp=0033346630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033346630&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0033346630

SP - 433

EP - 443

JO - Annual Symposium on Foundations of Computer Science - Proceedings

JF - Annual Symposium on Foundations of Computer Science - Proceedings

SN - 0272-5428

ER -