Effect of Maintaining Wavelength Continuity on Minimizing Network

Coding Resources in Optical Long-haul NetworksRamanathan S Thinniyam

Approaches to Minimize Network Coding Resources

• 2-Stage approach1. Minimize link cost (i.e. # of wavelengths)

required to maintain given connection through Integer Programming to obtain subgraph.

2. Minimize coding cost (i.e. # of coded wavelengths) in subgraph obtained from stage 1 using a Genetic Algorithm(GA).

• Multi-Objective Evolutionary Approach(MOEA)- Obtain a Pareto front of tradeoffs between link cost and coding cost. Specifically, we use the NSGA –II algorithm*

* K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II",IEEE Trans. Evol. Comput.,6(2):182–197(2002).

Wavelength Continuity

• Assume routing- dashed lines not routed, solid lines routed.• In optical networks, O/E/O equipment can be used for both

wavelength conversion as well to enable network coding.• If case 2 uses O/E/O equipment at node 1 to maintain

wavelength continuity, we can also code at this node if coding is allowed.

1

Case 1

1

Case 2

Simulation Results

• We perform experiments based on two different assumptions:

1.Hardware allowing wavelength conversion present at every node, cost of such conversion is zero (i.e. cost-free conversion).

2.O/E/O equipment present when conversion is needed (i.e. O/E/O based conversion). The cost of one or both coding and conversion at a node (or of a wavelength) is the same.

Results for O/E/O Based Continuity• The fitness criterion is changed from number of

coded wavelengths to number of wavelengths requiring O/E/O.

• # of wavelengths requiring O/E/O = # of solely converted wavelengths + # of coded wavelengths (coded wavelengths may or may not be converted).

• Results from 2 stage approach– never reduce O/E/O requirement to 0, – the number of O/E/O wavelengths on average is much

higher than the number of coded wavelengths in cost-free conversion.

– The cost of continuity is more O/E/O equipment

• Fraction of nodes where O/E/O equipment is required is much larger than fraction of wavelengths, when optimizing using number of wavelengths as criterion.

2-Stage Approach Result 1- Average Network Coding Requirement

• Conversion fraction=(Number of converted wavelengths)/(number of O/E/O wavelengths)

• Most problem instances show low conversion fraction < 1/3

2-Stage Approach Result 2 - Coding vs Conversion

2-Stage Approach Result 3 -Distribution of Number of O/E/O Wavelengths

2-Stage Approach Result 3 -Distribution of Number of O/E/O Wavelengths

2-Stage ApproachResult 4a- Comparing Cost-free vs O/E/O

2-Stage Approach Result 4b - Comparing Cost-free vs O/E/O

2-Stage ApproachResult 5- High Frequency Nodes

ARPANET

NSFNET

NJLATA

Nodes which were O/E/O nodes in the solution obtained in more than half the problem instances indicated in red.