Universal bounds on buffer size for packetizing fluid policies in input queued, crossbar switches

Michael Rosenblum, Michel X. Goemans, Vahid Tarokh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we consider a type of on-line, traffic scheduling problem in input queued, crossbar switches. The input to a problem, at each time step, is a set of desired traffic rates. These traffic rates in general cannot be exactly achieved since they assume arbitrarily small fractions of packets can be transmitted at each time step. The goal of the traffic scheduling problem is to closely approximate the given sequence of traffic rates by a sequence of switch uses in which only whole packets are sent. The focus of this paper is bounding the costs incurred in using such an approximation, in terms of the additional buffer size required. We establish universal bounds on the additional buffer size due to sending only whole packets; these bounds do not depend on the particular distribution of the input traffic, require no speedup, and guarantee 100% throughput. Specifically, for an N × N input queued, crossbar switch, an on-line, packetizing algorithm is presented that guarantees 100% throughput with a buffer requirement of (N + 1) 2 /4 packets per input port with no speedup. The algorithm can be improved to run in O(N log N) time, using a fast algorithm for edge-coloring bipartite multi-graphs. In the reverse direction, it is shown for an N × N input queued, crossbar switch, that any on-line, packetizing algorithm with no speedup requires a buffer size of N/e - 2 packets per input port. We also extend the main packetizing algorithm in this paper to a general class of switch architectures.

Original languageEnglish (US)
Title of host publicationIEEE INFOCOM 2004 - Conference on Computer Communications - Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies
Pages1126-1134
Number of pages9
DOIs
StatePublished - Nov 22 2004
Externally publishedYes
EventIEEE INFOCOM 2004 - Conference on Computer Communications - Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies - Hongkong, China
Duration: Mar 7 2004Mar 11 2004

Publication series

NameProceedings - IEEE INFOCOM
Volume2
ISSN (Print)0743-166X

Other

OtherIEEE INFOCOM 2004 - Conference on Computer Communications - Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies
CountryChina
CityHongkong
Period3/7/043/11/04

Keywords

  • Combinatorics
  • Deterministic network calculus
  • Graph theory

ASJC Scopus subject areas

  • Computer Science(all)
  • Electrical and Electronic Engineering

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