### Abstract

We consider the problems of online and stochastic packet queuing in a distributed system of n nodes with queues, where the communication between the nodes is done via a multiple access channel. In each round, an arbitrary number of packets can be injected into the system, each to an arbitrary node's queue. Two measures of performance are considered: the total number of packets in the system, called the total load, and the maximum queue size, called the maximum load. In the online setting, we develop a deterministic algorithm that is asymptotically optimal with respect to both complexity measures, in a competitive way. More precisely, the total load of our algorithm is bigger then the total load of any other algorithm, including centralized offline solutions, by only O(n ^{2}), while the maximum queue size of our algorithm is at most n times bigger than the maximum queue size of any other algorithm, with an extra additive O(n). The optimality for both measures is justified by proving the corresponding lower bounds. Next, we show that our algorithm is stochastically optimal for any expected injection rate smaller or equal to 1. To the best of our knowledge, this is the first solution to the stochastic queuing problem on a multiple access channel that achieves such optimality for the (highest possible) rate equal to 1.

Original language | English (US) |
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Title of host publication | Distributed Computing - 26th International Symposium, DISC 2012, Proceedings |

Pages | 121-135 |

Number of pages | 15 |

DOIs | |

State | Published - Nov 9 2012 |

Externally published | Yes |

Event | 26th International Symposium on Distributed Computing, DISC 2012 - Salvador, Brazil Duration: Oct 16 2012 → Oct 18 2012 |

### 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 | 7611 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 26th International Symposium on Distributed Computing, DISC 2012 |
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Country | Brazil |

City | Salvador |

Period | 10/16/12 → 10/18/12 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Distributed Computing - 26th International Symposium, DISC 2012, Proceedings*(pp. 121-135). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7611 LNCS). https://doi.org/10.1007/978-3-642-33651-5_9