1. Optical networks: Basics of WDM

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

3. Optical networks - 2nd generation
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

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

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

6. Lightpaths
ADM
ADM
Data in electronic form
Data in electronic form

7. A virtual topology

8. Lightpaths
Valid coloring p1 p2

9. The Routing Problem Input : Output: A graph G=(V,E)
A set or sequence of node pairs (ai,bi)
Output:
A set or sequence of paths pi =(ai, v1, …, bi)

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)=|Pe|
The (maximum, minimum, average) load on the network:

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. Routing and WLA (RLA/WRA)
Input :
A graph G=(V,E)
A set or sequence of node pairs (ai,bi)
Output:
A set or sequence of paths pi =(ai, v1, …, bi)
A coloring w of the paths:
Constraint:

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
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 p1, …, 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: