### Abstract

We analyse a model of exhaustion of shared memory. The memory usage of a finite number of dynamic data structures is modelled as a Markov chain, and the asymptotics of the expected time until memory exhaustion are worked out, in the limit when memory availability and memory needs scale proportionately, and are taken to infinity. This stochastic model subsumes the model of colliding stacks previously treated by the authors, and gives rise to difficult mathematical problems. However, analytic results can be obtained in the limit. Our analysis uses a technique of matched asymptotic expansions introduced by Naeh et al. [11]. The technique is applicable to other stochastically modelled discrete algorithms.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings |

Publisher | Springer Verlag |

Pages | 494-505 |

Number of pages | 12 |

Volume | 709 LNCS |

ISBN (Print) | 9783540571551 |

State | Published - Jan 1 1993 |

Event | 3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada Duration: Aug 11 1993 → Aug 13 1993 |

### 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 | 709 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Workshop on Algorithms and Data Structures, WADS 1993 |
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Country | Canada |

City | Montreal |

Period | 8/11/93 → 8/13/93 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings*(Vol. 709 LNCS, pp. 494-505). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 709 LNCS). Springer Verlag.

**The exhaustion of shared memory : Stochastic results.** / Maier, Robert S; Schott, René.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings.*vol. 709 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 709 LNCS, Springer Verlag, pp. 494-505, 3rd Workshop on Algorithms and Data Structures, WADS 1993, Montreal, Canada, 8/11/93.

}

TY - GEN

T1 - The exhaustion of shared memory

T2 - Stochastic results

AU - Maier, Robert S

AU - Schott, René

PY - 1993/1/1

Y1 - 1993/1/1

N2 - We analyse a model of exhaustion of shared memory. The memory usage of a finite number of dynamic data structures is modelled as a Markov chain, and the asymptotics of the expected time until memory exhaustion are worked out, in the limit when memory availability and memory needs scale proportionately, and are taken to infinity. This stochastic model subsumes the model of colliding stacks previously treated by the authors, and gives rise to difficult mathematical problems. However, analytic results can be obtained in the limit. Our analysis uses a technique of matched asymptotic expansions introduced by Naeh et al. [11]. The technique is applicable to other stochastically modelled discrete algorithms.

AB - We analyse a model of exhaustion of shared memory. The memory usage of a finite number of dynamic data structures is modelled as a Markov chain, and the asymptotics of the expected time until memory exhaustion are worked out, in the limit when memory availability and memory needs scale proportionately, and are taken to infinity. This stochastic model subsumes the model of colliding stacks previously treated by the authors, and gives rise to difficult mathematical problems. However, analytic results can be obtained in the limit. Our analysis uses a technique of matched asymptotic expansions introduced by Naeh et al. [11]. The technique is applicable to other stochastically modelled discrete algorithms.

UR - http://www.scopus.com/inward/record.url?scp=84916567812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84916567812&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540571551

VL - 709 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 494

EP - 505

BT - Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings

PB - Springer Verlag

ER -