Rate Region Analysis for Uniform Fractional Routing Networks

LIU Yan-tao; LIU Heng

doi:10.3969/j.issn.0372-2112.2018.08.011

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Rate Region Analysis for Uniform Fractional Routing Networks

更新时间：2025-07-16

- Rate Region Analysis for Uniform Fractional Routing Networks
- Acta Electronica Sinica Vol. 46, Issue 8, Pages: 1876-1883(2018)
- 作者机构：
  
  1. 渤海大学工学院,辽宁,锦州,121013
  2. 北京理工大学信息与电子学院,北京,100081
  3. 渤海大学工学院,辽宁,锦州,121013
  4. 北京理工大学信息与电子学院,北京,100081
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2018.08.011
  CLC： TN915
- Published Online：25 August 2018，
  
  Published：2018
- 稿件说明：
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LIU Yan-tao, LIU Heng. Rate Region Analysis for Uniform Fractional Routing Networks[J]. Acta Electronica Sinica, 2018, 46(8): 1876-1883.
DOI：

LIU Yan-tao, LIU Heng. Rate Region Analysis for Uniform Fractional Routing Networks[J]. Acta Electronica Sinica, 2018, 46(8): 1876-1883. DOI： 10.3969/j.issn.0372-2112.2018.08.011.

摘要

均匀分数路由网络是指网络边传输的数据包具有相同的维数，且该维数与信源消息的维数可以不同.已知分数路由网络的容量域是多维欧式空间中的多胞体，但对各种业务模式网络的容量域的计算尚缺乏有效的可操作方法.本文研究了三种业务模式的容量域计算方法：针对多重单播，提出了基于缩减图、合并缩减图和虚拟节点的方法；针对一重组播，提出了基于子树分解和组合设计的方法；针对二重混合网络，提出了基于凸多边形极点的方法.除了理论证明之外，还举了大量样例演示这些方法的正确性.

Abstract

If packets are with identical dimensions

which may be different from the dimensions of source messages

the network is called uniform fractional routing network.The rate region of a fractional routing network is a polytope in a multidimensional Euclidean space

but effective implementable methods are still missing to calculate the region for networks with different traffic patterns.This paper studied rate region analysis methods for three traffic patterns:For multiple unicasts

a method based on reduced graph

union reduced graph

and virtual node was proposed;For a single multicast

it was based on subtree decomposition and combinatorial design;For a pattern mixed of two flows

the polygon region was drawn by determining all extreme points.Correctness of these methods was proved in theory and illustrated by examples.

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