## Abstract

We consider model based estimates for set-up time. The general setting we are interested in is the following: given a disk and a sequence of read/write requests to certain locations, we would like to know the total time of transitions (set-up time) when these requests are served in an orderly fashion. The problem becomes nontrivial when we have, as is typically the case, only the counts of requests to each location rather then the whole input, in which case we can only hope to estimate the required time. Models that estimate the set-up time have been suggested and heavily used as far back as the sixties. However, not much theory exists to enable a qualitative understanding of such models. To this end we introduce several properties through which we can study different models such as (i) super-additivity which means that the set-up time estimate decreases as the input data is refined (ii) monotonicity which means that more activity produces more set-up time, and (iii) an approximation guarantee for the estimate with respect to the worst possible time. We provide criteria for super-additivity and monotonicity to hold for popular models such as the independent reference model (IRM). The criteria show that the estimate produced by these models will be monotone for any reasonable system. We also show that the IRM based estimate functions, upto a factor of 2, as a worst case estimate to the actual set-up time. To establish our theoretical results we use the theory of finite metric spaces, and en route show a result of independent interest in that theory, which is a strengthening of a theorem of Kelly [4] about the properties of metrics that are formed by concave functions on the line.

Original language | English |
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Title of host publication | Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings |

Publisher | Springer Verlag |

Pages | 387-397 |

Number of pages | 11 |

ISBN (Print) | 3540369252, 9783540369257 |

DOIs | |

State | Published - 1 Jan 2006 |

Event | 12th Annual International Conference on Computing and Combinatorics, COCOON 2006 - Taipei, Taiwan, Province of China Duration: 15 Aug 2006 → 18 Aug 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4112 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 12th Annual International Conference on Computing and Combinatorics, COCOON 2006 |
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Country/Territory | Taiwan, Province of China |

City | Taipei |

Period | 15/08/06 → 18/08/06 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)