# MatPlanWDM v0.5

### Pablo Pavon Mariño (view profile)

29 Jan 2007 (Updated )

Educational network planning tool for the RWA problem in WDM networks (MILP and heuristic based)

libraryVTD_RLDA.m
```% RLDA (Random Logical Design Algorithm)
%
% Usage: [exitFlag lightpathTable lightpathRoutingMatrix  numberOfOccupiedTWCs numberOfOccupiedTxs numberOfOccupiedRxs] =
% libraryVTD_RLDA(traff_trafficMatrix,phys)
%
% Abstract: RLDA is the simplest heuristic algorithm to solve the vitual
% topology design (VTD) problem, but very useful in terms of comparison
% proposes. It places logical edges entirely at random, subject to finding
% a lightpath for each edge and not violating degree constraints, but
% ignoring traffic matrix altogether.
%
% This method solves the first three of the four classic subproblems into
% which the Virtual Topology Design Problem is possible to decompose:
%
% 1) Virtual Topology Subproblem
% 2) Lightpath Routing Subproblem
% 3) Wavelength Assignment Subproblem
% 4) Traffic Routing (over the Virtual Topology) Subproblem
%
% NOTE: This algorithm does not solve the traffic flow routing over the
% virtual topology. For this purpose, it is necessary to apply some flow
% routing method over the virtual topology obtained with this function.
%
% Arguments:
% o	In:
%   traff_trafficMatrix(NxN): Average traffic flow offered between node
%    pairs. The Traffic Matrix is a two-dimensional matrix with N (N:
%    number of nodes) rows and N columns. An entry(s,d) means the average
%    traffic flow from node 's' to node 'd', expressed in Gbps. The main
%    diagonal is full of 0s.
%
%  . phys: Phys Structure. More information about netState in section
%    "Structure of phys variable" from Help.
%
%
% o	Out:
%  . exitFlag:
%           0, if it is possible to design the virtual topology
%           1, if the virtual topology design is NOT FEASIBLE as there is
%              no sufficient resources to establish any lightpath.
%
%  . lightpathTable(L,3): L-by-3 integer matrix. Each row is a
%    lightpath 'l', where the first column is the serial number of the
%    lightpath, the second and third columns of each row are
%    theorigin node 'i' and destination node 'j' of this lightpath 'l'
%    respectively and L is the number of lightpaths of the virtual
%    topology.
%
% .  lightpathRoutingMatrix (L,M): L-by-M integer matrix where L
%    is the number of lightpaths and M is the number of physical fibre
%    links. Each row is a lightpath 'l' and each column is a physical link
%    'm'. If a lightpath 'l' uses a physical link 'm' with a certain
%    wavelength 'w', the entry (l,m) is  equal to 'w'. If no physical link
%    is used by the lightpath 'l', the entry is equal to '0'.
%
%  . numberOfOccupiedTxs (Nx1): N integer vector where N is the
%    number of nodes. Each position 'i' is the number of occupied (used)
%    transmitters that the node with ID 'i' has.
%
%  . numberOfOccupiedRxs (Nx1): N integer vector where N is the
%    number of nodes. Each position 'i' is the number of occupied (used)
%    receivers that the node with ID 'i' has.
%
%  . numberOfOccupiedTWCs (Nx1): N integer vector where N is the
%    number of nodes. Each position 'i' is the number of occupied (used)
%    converters that the node with ID 'i' has.
%

function [exitFlag lightpathTable lightpathRoutingMatrix  numberOfOccupiedTWCs numberOfOccupiedTxs numberOfOccupiedRxs] =  libraryVTD_RLDA(traff_trafficMatrix,phys)

%MAIN VARIABLES*********************************************************

exitFlag = 0;

numberOfNodes = phys.N;

lightpathTable=[];
lightpathRoutingMatrix=[];
numberOfOccupiedTxs = zeros (numberOfNodes,1);
numberOfOccupiedRxs = zeros (numberOfNodes,1);
numberOfOccupiedTWCs = zeros (numberOfNodes,1); % does not change as this is a non-wavelength-converting heuristic

%"freeWavelengths" is a matrix, where rows are each link
%((1,1)(2,1)(3,1)(4,1)(1,2)(2,2)...) and columns are a specifical
%wavelength: w0, w1, w2... Each value is 0 or 1 if that is free
freeWavelengths(i,1:phys.numberWavelengthPerFiber(i))=1;
end

%ALGORITHM DEVELOPMENT*********************************************

numberOfLightpaths=0;

numberOfIterations=numberOfNodes^2-numberOfNodes;%total number of iterations
nodePairs=zeros(numberOfIterations,2);

%We save all node pairs in a variable with two columns and order them in random sequence
aux=diag(ones(1,numberOfNodes));
[nodePairs(:,1),nodePairs(:,2)]=find(aux==0);
randomOrder=randperm(length(nodePairs));
%All node pairs are ordered randomly
nodePairs=nodePairs(randomOrder,:);

%Main loop. It works along such iterations as number of node pairs.
for m=1:numberOfIterations,

%FIRST CONDITION: A TRANSMITER IN SOURCE NODE AND A RECEIVER IN DESTINATION NODE
if(numberOfOccupiedRxs(nodePairs(m,2))<phys.numberRxPerNode(nodePairs(m,2)) &&...
numberOfOccupiedTxs(nodePairs(m,1))<phys.numberTxPerNode(nodePairs(m,1))),

%SECOND CONDITION: IT'S NECESSARY THE SAME WAVELENGTH IN ALL physical ROUTE
[sequenceOfSPFLinkIds,sequenceOfSPFNodeIds , totalCost] = ....
libraryGraph_shortestPath (linkTable , nodePairs(m,1) , nodePairs(m,2));

%A matrix such "freeWavelengths" is built. It only contains the links of
%the physical route. Now we can check which of them are availables to be used.
usedWavelength=0;

for i=1:size(freeWavelengthsOnRoute,2)%we check all wavelengths
%The column with all-ones is the used one as wavelength
if(freeWavelengthsOnRoute(:,i)==ones(size(freeWavelengthsOnRoute,1),1)),
usedWavelength=i;%the wavelength is established

%trasmitters and receivers are updated in source and destination nodes
numberOfOccupiedTxs(nodePairs(m,1))=numberOfOccupiedTxs(nodePairs(m,1))+1;
numberOfOccupiedRxs(nodePairs(m,2))=numberOfOccupiedRxs(nodePairs(m,2))+1;

%freeWavelengths is updated when the used wavelength which is occupied (0)

%virtualTopology is updated with the new lightpath
serialNumberOfLightpaths=size(lightpathTable,1)+1;
lightpathTable=[lightpathTable; [serialNumberOfLightpaths nodePairs(m,1) nodePairs(m,2)]];

lightpathRoutingMatrix=[lightpathRoutingMatrix; currentLightpathRouting];
numberOfLightpaths=numberOfLightpaths+1;

break%we don't continue checking wavelengths when a successful one has been found
end
end
end
end%End of the main loop

if isempty(lightpathTable) || isempty(lightpathRoutingMatrix), exitFlag = 1; end  % there is no sufficient resources to establish any lightpath.
```