### Abstract

We study the problem of scheduling parallel machines online, allowing preemptions while disallowing migration of jobs that have been scheduled on one machine to another. For a given job, we measure the quality of service provided by an algorithm by the stretch of the job, defined as the ratio between the amount of time spent by the job in the system (the response time) and its processing time. For a sequence of jobs, we measure the performance of an algorithm by the average stretch achieved over all jobs. The scheduling goal is to minimize the average stretch. This problem is of relevance in many applications. e.g., wireless data servers and distributed server systems in wired networks. We prove an O(1) competitive ratio for this problem. The algorithm for which we prove this result is the one proposed in Awerbuch et al. (Proceedings of the ACM Symposium on the Theory of Computing (STOC '99), 1999, pp. 198-205) that has (tight) logarithmic competitive ratio for minimizing the average response time. Thus, the algorithm in Awerbuch et al. (Proceedings of the ACM Symposium on the Theory of Computing (STOC '99), 1999. pp. 198-205) simultaneously performs well for average response time as well as average stretch. We prove the O(1) competitive ratio against an adversary who not only knows the entire input ahead of time, but is also allowed to migrate jobs. Thus, our result shows that migration is not necessary to be competitive for minimizing average stretch; in contrast, we prove that preemption is essential, even if randomization is allowed.

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

Pages (from-to) | 80-95 |

Number of pages | 16 |

Journal | Journal of Computer and System Sciences |

Volume | 68 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2004 |

### Fingerprint

### Keywords

- Average stretch
- Migration
- Scheduling

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Journal of Computer and System Sciences*,

*68*(1), 80-95. https://doi.org/10.1016/j.jcss.2003.06.001

**Average stretch without migration.** / Becchetti, Luca; Leonardi, Stefano; Muthukrishnan, Shanmugavelayutham.

Research output: Contribution to journal › Article

*Journal of Computer and System Sciences*, vol. 68, no. 1, pp. 80-95. https://doi.org/10.1016/j.jcss.2003.06.001

}

TY - JOUR

T1 - Average stretch without migration

AU - Becchetti, Luca

AU - Leonardi, Stefano

AU - Muthukrishnan, Shanmugavelayutham

PY - 2004/1/1

Y1 - 2004/1/1

N2 - We study the problem of scheduling parallel machines online, allowing preemptions while disallowing migration of jobs that have been scheduled on one machine to another. For a given job, we measure the quality of service provided by an algorithm by the stretch of the job, defined as the ratio between the amount of time spent by the job in the system (the response time) and its processing time. For a sequence of jobs, we measure the performance of an algorithm by the average stretch achieved over all jobs. The scheduling goal is to minimize the average stretch. This problem is of relevance in many applications. e.g., wireless data servers and distributed server systems in wired networks. We prove an O(1) competitive ratio for this problem. The algorithm for which we prove this result is the one proposed in Awerbuch et al. (Proceedings of the ACM Symposium on the Theory of Computing (STOC '99), 1999, pp. 198-205) that has (tight) logarithmic competitive ratio for minimizing the average response time. Thus, the algorithm in Awerbuch et al. (Proceedings of the ACM Symposium on the Theory of Computing (STOC '99), 1999. pp. 198-205) simultaneously performs well for average response time as well as average stretch. We prove the O(1) competitive ratio against an adversary who not only knows the entire input ahead of time, but is also allowed to migrate jobs. Thus, our result shows that migration is not necessary to be competitive for minimizing average stretch; in contrast, we prove that preemption is essential, even if randomization is allowed.

AB - We study the problem of scheduling parallel machines online, allowing preemptions while disallowing migration of jobs that have been scheduled on one machine to another. For a given job, we measure the quality of service provided by an algorithm by the stretch of the job, defined as the ratio between the amount of time spent by the job in the system (the response time) and its processing time. For a sequence of jobs, we measure the performance of an algorithm by the average stretch achieved over all jobs. The scheduling goal is to minimize the average stretch. This problem is of relevance in many applications. e.g., wireless data servers and distributed server systems in wired networks. We prove an O(1) competitive ratio for this problem. The algorithm for which we prove this result is the one proposed in Awerbuch et al. (Proceedings of the ACM Symposium on the Theory of Computing (STOC '99), 1999, pp. 198-205) that has (tight) logarithmic competitive ratio for minimizing the average response time. Thus, the algorithm in Awerbuch et al. (Proceedings of the ACM Symposium on the Theory of Computing (STOC '99), 1999. pp. 198-205) simultaneously performs well for average response time as well as average stretch. We prove the O(1) competitive ratio against an adversary who not only knows the entire input ahead of time, but is also allowed to migrate jobs. Thus, our result shows that migration is not necessary to be competitive for minimizing average stretch; in contrast, we prove that preemption is essential, even if randomization is allowed.

KW - Average stretch

KW - Migration

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=0842278862&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0842278862&partnerID=8YFLogxK

U2 - 10.1016/j.jcss.2003.06.001

DO - 10.1016/j.jcss.2003.06.001

M3 - Article

VL - 68

SP - 80

EP - 95

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

IS - 1

ER -