Buffer management for packets with processing times

Yossi Azar; Oren Gilon

doi:10.1007/978-3-662-48350-3_5

Buffer management for packets with processing times

Yossi Azar, Oren Gilon

School of Computer Science

Tel Aviv University

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

Abstract

We discuss the well known job scheduling problem with release times and deadlines, alongside an extended model - buffer management for packets with processing requirements. For job scheduling, an (Formula presented) lower bound for any randomized preemptive algorithm was shown by Irani and Canetti (1995), where κ is the the maximum job duration or the maximum job value (the minimum is assumed to be 1). The proof of this well-known result is fairly elaborate and involved. In contrast, we show a significantly improved lower bound of Ω(log κ) using a simple proof. Our result matches the easy upper bound and closes a gap which was supposedly open for 20 years. We also discuss an interesting extension of job scheduling (for tight jobs). We discuss the problem of handling a FIFO buffer of a limited capacity, where packets arrive over time and may be preempted. Most of the work in buffer management considers the case where each packet has unit processing requirement. We consider a model where packets require some number of processing cycles before they can be transmitted.We aim to maximize the value of transmitted packets. We show an Ω(log κ log log κ) lower bound on the competitive ratio of randomized algorithms in this setting.We also present bounds for several special cases. For packets with unit values we also show a ϕ ≈ 1.618 lower bound on the competitive ratio of deterministic algorithms, and a 2-competitive algorithm for this problem. For the case of packets with constant densities we present a 4-competitive algorithm.

Original language	English
Title of host publication	Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
Editors	Nikhil Bansal, Irene Finocchi
Publisher	Springer Verlag
Pages	47-58
Number of pages	12
ISBN (Print)	9783662483497
DOIs	https://doi.org/10.1007/978-3-662-48350-3_5
State	Published - 2015
Event	23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9294

Conference

Conference	23rd European Symposium on Algorithms, ESA 2015
Country/Territory	Greece
City	Patras
Period	14/09/15 → 16/09/15

Keywords

Buffer management
Competitive analysis
Deadlines
Job scheduling
Online algorithms

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-662-48350-3_5

Cite this

Azar, Y., & Gilon, O. (2015). Buffer management for packets with processing times. In N. Bansal, & I. Finocchi (Eds.), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings (pp. 47-58). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_5

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title = "Buffer management for packets with processing times",

abstract = "We discuss the well known job scheduling problem with release times and deadlines, alongside an extended model - buffer management for packets with processing requirements. For job scheduling, an (Formula presented) lower bound for any randomized preemptive algorithm was shown by Irani and Canetti (1995), where κ is the the maximum job duration or the maximum job value (the minimum is assumed to be 1). The proof of this well-known result is fairly elaborate and involved. In contrast, we show a significantly improved lower bound of Ω(log κ) using a simple proof. Our result matches the easy upper bound and closes a gap which was supposedly open for 20 years. We also discuss an interesting extension of job scheduling (for tight jobs). We discuss the problem of handling a FIFO buffer of a limited capacity, where packets arrive over time and may be preempted. Most of the work in buffer management considers the case where each packet has unit processing requirement. We consider a model where packets require some number of processing cycles before they can be transmitted.We aim to maximize the value of transmitted packets. We show an Ω(log κ log log κ) lower bound on the competitive ratio of randomized algorithms in this setting.We also present bounds for several special cases. For packets with unit values we also show a ϕ ≈ 1.618 lower bound on the competitive ratio of deterministic algorithms, and a 2-competitive algorithm for this problem. For the case of packets with constant densities we present a 4-competitive algorithm.",

keywords = "Buffer management, Competitive analysis, Deadlines, Job scheduling, Online algorithms",

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Azar, Y & Gilon, O 2015, Buffer management for packets with processing times. in N Bansal & I Finocchi (eds), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9294, Springer Verlag, pp. 47-58, 23rd European Symposium on Algorithms, ESA 2015, Patras, Greece, 14/09/15. https://doi.org/10.1007/978-3-662-48350-3_5

Buffer management for packets with processing times. / Azar, Yossi; Gilon, Oren.
Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. ed. / Nikhil Bansal; Irene Finocchi. Springer Verlag, 2015. p. 47-58 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294).

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

TY - GEN

T1 - Buffer management for packets with processing times

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AU - Gilon, Oren

N1 - Publisher Copyright: ©Springer-Verlag Berlin Heidelberg 2015.

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N2 - We discuss the well known job scheduling problem with release times and deadlines, alongside an extended model - buffer management for packets with processing requirements. For job scheduling, an (Formula presented) lower bound for any randomized preemptive algorithm was shown by Irani and Canetti (1995), where κ is the the maximum job duration or the maximum job value (the minimum is assumed to be 1). The proof of this well-known result is fairly elaborate and involved. In contrast, we show a significantly improved lower bound of Ω(log κ) using a simple proof. Our result matches the easy upper bound and closes a gap which was supposedly open for 20 years. We also discuss an interesting extension of job scheduling (for tight jobs). We discuss the problem of handling a FIFO buffer of a limited capacity, where packets arrive over time and may be preempted. Most of the work in buffer management considers the case where each packet has unit processing requirement. We consider a model where packets require some number of processing cycles before they can be transmitted.We aim to maximize the value of transmitted packets. We show an Ω(log κ log log κ) lower bound on the competitive ratio of randomized algorithms in this setting.We also present bounds for several special cases. For packets with unit values we also show a ϕ ≈ 1.618 lower bound on the competitive ratio of deterministic algorithms, and a 2-competitive algorithm for this problem. For the case of packets with constant densities we present a 4-competitive algorithm.

AB - We discuss the well known job scheduling problem with release times and deadlines, alongside an extended model - buffer management for packets with processing requirements. For job scheduling, an (Formula presented) lower bound for any randomized preemptive algorithm was shown by Irani and Canetti (1995), where κ is the the maximum job duration or the maximum job value (the minimum is assumed to be 1). The proof of this well-known result is fairly elaborate and involved. In contrast, we show a significantly improved lower bound of Ω(log κ) using a simple proof. Our result matches the easy upper bound and closes a gap which was supposedly open for 20 years. We also discuss an interesting extension of job scheduling (for tight jobs). We discuss the problem of handling a FIFO buffer of a limited capacity, where packets arrive over time and may be preempted. Most of the work in buffer management considers the case where each packet has unit processing requirement. We consider a model where packets require some number of processing cycles before they can be transmitted.We aim to maximize the value of transmitted packets. We show an Ω(log κ log log κ) lower bound on the competitive ratio of randomized algorithms in this setting.We also present bounds for several special cases. For packets with unit values we also show a ϕ ≈ 1.618 lower bound on the competitive ratio of deterministic algorithms, and a 2-competitive algorithm for this problem. For the case of packets with constant densities we present a 4-competitive algorithm.

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DO - 10.1007/978-3-662-48350-3_5

M3 - منشور من مؤتمر

SN - 9783662483497

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

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BT - Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings

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ER -

Azar Y, Gilon O. Buffer management for packets with processing times. In Bansal N, Finocchi I, editors, Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Springer Verlag. 2015. p. 47-58. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-48350-3_5

Buffer management for packets with processing times

Abstract

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Conference

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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