Module 20 : WDM Networks
Lecture      : WDM Networks
  Wavelength Management in a Router:
 

If the pattern of traffic in the network is known in advance and the variations take place over a long period of time, one can optimize network resources and arrive at a virtual network. Such a router is called a static router. The continuity condition is to be satisfied and only one wavelength may be used per route.
The problem of wavelength management incorporating continuity condition is same as working out a Latin square . A Latin square is an $ N\times N$matrix in which $ N$distinct objects are placed such that no two elements of a given row (or of a column) have identical objects placed in them. (Students familiar with the game of Sudoku will notice the resemblance.) Mathematically, a Latin square is a matrix $ M$defined as follows:

$\displaystyle M = [a_{ij}]\ \ (1\le i,j\le N)$

such that

$\displaystyle a_{ij}$

$\displaystyle =$

$\displaystyle a_{ik}\ \ {\rm for}\ \ j\ne k$

 

$\displaystyle a_{ij}$

$\displaystyle =$

$\displaystyle a_{kj}\ \ {\rm for}\ \ i\ne k$

 

The number of distinct Latin squares grows exponentially with increasing $ N$. For instance, there are only 12 squares of order 3, 576 of order 4 but over $ 5\times 10^{28}$squares of order 9. Examples of two Latin square of order 4 are given below.

\includegraphics{wdm25}
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