## Abstract

In this paper we improve the approximation ratio for the problem of scheduling packets on line networks with bounded buffers with the aim of maximizing the throughput. Each node in the network has a local buffer of bounded size B, and each edge (or link) can transmit a limited number c of packets in every time unit. The input to the problem consists of a set of packet requests, each defined by a source node, a destination node, and a release time. We denote by n the size of the network. A solution for this problem is a schedule that delivers (some of the) packets to their destinations without violating the capacity constraints of the network (buffers or edges). Our goal is to design an efficient algorithm that computes a schedule that maximizes the number of packets that arrive to their respective destinations. We give a randomized approximation algorithm with constant approximation ratio for the case where the buffer-size to link-capacity ratio, B/c, does not depend on the input size. This improves over the previously best result of O(log^{∗} n) [11]. Our improvement is based on a new combinatorial lemma that we prove, stating, roughly speaking, that if packets are allowed to stay put in buffers only a limited number of time steps, 2d, where d is the longest source-destination distance, then the optimal solution is decreased by only a constant factor. This claim was not previously known in the integral (unsplitable, zero-one) case, and may find additional applications for routing and scheduling algorithms. While we are not able to give the same improvement for the related problem when packets have hard deadlines, our algorithm does support "soft deadlines". That is, if packets have deadlines, we achieve a constant approximation ratio when the produced solution is allowed to miss deadlines by at most logn time units.

Original language | English |
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Title of host publication | 24th Annual European Symposium on Algorithms, ESA 2016 |

Editors | Christos Zaroliagis, Piotr Sankowski |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770156 |

DOIs | |

State | Published - 1 Aug 2016 |

Externally published | Yes |

Event | 24th Annual European Symposium on Algorithms, ESA 2016 - Aarhus, Denmark Duration: 22 Aug 2016 → 24 Aug 2016 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 57 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 24th Annual European Symposium on Algorithms, ESA 2016 |
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Country/Territory | Denmark |

City | Aarhus |

Period | 22/08/16 → 24/08/16 |

### Bibliographical note

Publisher Copyright:© Guy Even, Moti Medina, and Adi Rosén.

## Keywords

- Admission control
- Approximation algorithms
- Linear programming
- Packet scheduling
- Randomized rounding