Download presentation

Presentation is loading. Please wait.

Published byDaisy Croke Modified about 1 year ago

1
1 Optical networks: Basics of WDM

2
2 the fiber serves as a transmission medium Electronic switch Optic fiber Optical networks - 1 st generation

3
3 Routing in the optical domain Two complementing technologies: - Wavelength Division Multiplexing (WDM): Transmission of data simultaneously at multiple wavelengths over same fiber - Optical switches: the output port is determined according to the input port and the wavelength Optical networks - 2 nd generation

4
4 Wavelength Division Multiplexing (WDM) Directed: Symmetric: Undirected: Optic Fiber

5
5 Optical Switches No two inputs with the same wavelength should be routed on the same edge.

6
6 Lightpaths ADM Data in electronic form

7
7 A virtual topology

8
8 Lightpaths p1 p2 Valid coloring

9
9 The Routing Problem Input : A graph G=(V,E) A set or sequence of node pairs (a i,b i ) Output: A set or sequence of paths p i =(a i, v 1, …, b i )

10
10 The Load Given a graph G=(V,E) and a set P of paths on the graph, we define: for any edge e of the graph: the load on this edge l(e)=|P e | The (maximum, minimum, average) load on the network:

11
11 Wavelength Assignment Problem (WLA) Input: A graph G=(V,E). A set or sequence of paths P. Output: A coloring w of the paths: Constraint:

12
12 Routing and WLA (RLA/WRA) Input : A graph G=(V,E) A set or sequence of node pairs (a i,b i ) Output: A set or sequence of paths p i =(a i, v 1, …, b i ) A coloring w of the paths: Constraint:

13
13 Cost Measure: # of colors For any legal coloring w of the paths:

14
Static vs. Dynamic vs. Incremental Static: The input is a set (of pairs or paths), the algorithm calculates its output based on the input. Incremental (Online): The input is a sequence of input elements (pairs or paths). It is supplied to the algorithm one element at a time. The output corresponding to the input element is calculated w/o knowledge of the subsequent input elements

15
Static vs. Dynamic vs. Incremental Dynamic: Similar to incremental The sequence may contain deletion requests for previous elements.

16
WLA (A trivial lower bound) For any instance of the WLA problem: W>=L. Proof: Consider an edge e, such that L=l(e). There are L paths p 1, …, p |L| using e, because the paths are simple. Therefore :

17
WLA (A trivial lower bound) For some instances W > L. L=2 W=3

18
Static WLA on Path Topologies The GREEDY algorithm: // The set of integers for i = 1 to |V| do for each path p=(x,i) do for each path p=(i,x) do

19
Static WLA on Path Topologies Let the value of after node i is processed. Clearly, Prove by induction on i that Therefore:

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google