Algorithm 1
Adaptive Modulation for Optical Transmission
Input: Data rate D; Candidate modulation levels M; |
BER threshold without using forward error correction (FEC) ; |
MZM required voltage difference ; |
Laser output power upper bound ; |
Lowest laser output power as initial solution; |
Output: Return optimal solution for M; |
1: Computing the required lowest number of subcarriers L for each candidate modulation level in M through , where and is taken as the base capacity of one subcarrier using BPSK; |
2: Calculating BER for each candidate modulation level in ; |
3: If all elements in , then the is the optimal solution for corresponding modulation levels M; |
4: If not, increase corresponding () for modulation level whose , then go to step 2; |
5: return . |
Algorithm 2
Traffic Grooming
Input: Initial groomed traffic ; |
Step size ; Data rate capacity of transponder ; |
Maximum grooming size (); |
Output: Groomed traffic matrix ; |
1: Sweeping maximum grooming size by searching for a traffic segment of smaller than ; that is, satisfying ; |
2: Finding any intermediate node between and , and the grooming size for incomplete must equal ; |
3: If and , then update the value by , , ; |
4: If incomplete remain, choosing any other intermediate node to perform grooming, and stop when ; |
5: Grooming traffic flows for all node pairs ; |
6: Increasing maximum grooming size with size , and repeat steps 1–5; |
7: return . |
Algorithm 3
Simulated Annealing
Input: Initial annealing temperature ; temperature decrement factor ; |
Final temperature ; Iteration number ; |
Output: Routing and modulation solution ; |
1: Generating uniformly distributed random matrix based on the network topology, and select it as initial random solution ; |
2: Performing traffic grooming for input traffic flows through Algorithm 2, and calculate OEO conversion cost for electronic switching; |
3: Performing spectrum allocation through routing and wavelength assignment according to a first-fit mechanism, and calculate fiber link costs and optical conversion costs ; |
4: Run adaptive modulation searching procedure in Algorithm 1 for corresponding , value of each lightpath. If no solution meets the , jump to step 6; |
5: Computing initial objective function for initial solution and probability of acceptance ; |
6: Generating new trail phase factor ; |
7: Repeat steps 3–5; |
8: Constraints in Eqs. (9)–(16) and decide whether a newly derived solution should be accepted or not. If the condition is met, the current stored solution is replaced with the new one, and the objective function is set to the new value. If not, it keeps the old solution; |
9: Decreasing temperature according to the cooling schedule ; |
10: Increasing iteration count , and repeat steps 3–9; |
11: return . |
Algorithm 4
Iterative Flipping
Input: Initial system state ; |
Output: Routing and modulation solution ; |
1: Performing traffic grooming for input traffic flows through Algorithm 2, and calculate OEO conversion cost for electronic switching; |
2: Performing spectrum allocation through routing and wavelength assignment according to a first-fit mechanism, and calculate fiber link costs and optical conversion costs ; |
3: Run adaptive modulation searching procedure in Algorithm 1 for corresponding , value of each lightpath. If no solution meets the , jump to step 5; |
4: Computing the objective function , where refers to the cost function defined in Eq. (8) corresponding to the power consumption at state ; |
5: Increasing the first modulation factor ; |
6: Recomputing the resulting power consumption by repeating steps 2–4; |
7: Whether the new power consumption value with corresponding is accepted or not is based on the constraints in Eqs. (9)–(16), along with the following criterion: , where is the current solution. When , is accepted; otherwise, reverts to its previous value; |
8: Keep increasing the candidate modulation level until all possible modulation levels for are explored; |
9: Increasing traffic segment and repeat steps 3–8, until all possible modulation levels for all traffic lightpaths are explored; |
10: Increasing the first routing factor , and repeating steps 2–9; |
11: Keep increasing first routing factor until all possible candidate paths for are explored; |
12: Increasing traffic segment and repeat steps 2–11, until all traffic lightpaths are explored; |
13: return . |
Table I
Base Traffic Matrix for 5-Node Network (in Units of Gbps; )
Node | 1 | 2 | 3 | 4 | 5 |
---|
1 | 0 | 8 | 14 | 10 | 8 |
2 | 8 | 0 | 12 | 6 | 12 |
3 | 14 | 12 | 0 | 10 | 4 |
4 | 10 | 6 | 10 | 0 | 16 |
5 | 8 | 12 | 4 | 16 | 0 |
Table II
Base Traffic Matrix for 8-Node Network (in Units of Gbps; )
Node | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|
1 | 0 | 4 | 4 | 2 | 20 | 6 | 8 | 4 |
2 | 4 | 0 | 6 | 6 | 2 | 2 | 2 | 8 |
3 | 4 | 6 | 0 | 10 | 12 | 8 | 6 | 58 |
4 | 2 | 6 | 10 | 0 | 26 | 2 | 2 | 4 |
5 | 20 | 2 | 12 | 26 | 0 | 30 | 6 | 2 |
6 | 6 | 2 | 8 | 2 | 30 | 0 | 2 | 2 |
7 | 8 | 2 | 6 | 2 | 6 | 2 | 0 | 6 |
8 | 4 | 2 | 58 | 4 | 2 | 2 | 6 | 0 |
Table III
Base Traffic Matrix for NSFNet (in Units of Gbps; )
Node | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|
1 | 0 | 2 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 2 |
2 | 2 | 0 | 2 | 2 | 8 | 4 | 2 | 6 | 4 | 6 | 2 | 6 | 2 | 4 |
3 | 2 | 2 | 0 | 2 | 4 | 4 | 11 | 20 | 6 | 2 | 2 | 2 | 2 | 4 |
4 | 2 | 2 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 4 | 2 | 2 | 2 | 2 |
5 | 2 | 8 | 4 | 2 | 0 | 4 | 4 | 7 | 4 | 4 | 2 | 6 | 2 | 6 |
6 | 4 | 4 | 4 | 2 | 4 | 0 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 4 |
7 | 2 | 2 | 11 | 2 | 4 | 2 | 0 | 9 | 4 | 20 | 2 | 8 | 2 | 4 |
8 | 2 | 6 | 20 | 2 | 7 | 2 | 9 | 0 | 27 | 7 | 4 | 4 | 4 | 4 |
9 | 4 | 4 | 6 | 2 | 4 | 4 | 4 | 27 | 0 | 50 | 2 | 9 | 4 | 2 |
10 | 2 | 6 | 2 | 4 | 4 | 2 | 20 | 7 | 50 | 0 | 2 | 2 | 4 | 2 |
11 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 2 | 2 | 0 | 2 | 2 | 51 |
12 | 2 | 6 | 2 | 2 | 6 | 2 | 8 | 4 | 9 | 2 | 2 | 0 | 2 | 47 |
13 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 2 | 2 | 0 | 2 |
14 | 2 | 4 | 4 | 2 | 6 | 4 | 4 | 4 | 2 | 2 | 51 | 47 | 2 | 0 |
Table IV
Spectrum Utilization for 5-Node Network With Static Traffic
Load | Algorithm | Average Spectrum Utilization (%) |
---|
0.4 Tbps | | | | | | |
Fixed via SA, | 7.4 | 7.4 | 7.4 | N/A | N/A |
Fixed via SA, | 8.2 | 7.8 | 7.4 | N/A | N/A |
Adaptive via SA, | 6.9 | 6.9 | 6.9 | N/A | N/A |
Adaptive via SA, | 7.5 | 7.3 | 6.5 | N/A | N/A |
Adaptive via IF, | 8.5 | 6.7 | N/A | N/A | N/A |
Adaptive via ES, | N/A | N/A | N/A | 6.9 | 6.3 |
2 Tbps | | | | | | |
Fixed via SA, | 10.3 | 10.3 | 10.3 | N/A | N/A |
Fixed via SA, | 11.5 | 10.9 | 10.2 | N/A | N/A |
Adaptive via SA, | 10.1 | 10.1 | 10.1 | N/A | N/A |
Adaptive via SA, | 10.7 | 10.5 | 9.8 | N/A | N/A |
Adaptive via IF, | 11.7 | 9.5 | N/A | N/A | N/A |
Adaptive via ES, | N/A | N/A | N/A | 9.8 | 9.4 |
Table V
Spectrum Utilization for 5-Node Network With Dynamic Traffic
Load | Algorithm | Average Spectrum Utilization (%) |
---|
0.66 Tbps | | | | | | |
Fixed via SA, | 8.2 | 8.2 | 8.2 | N/A | N/A |
Fixed via SA, | 9.0 | 8.6 | 8.0 | N/A | N/A |
Adaptive via SA, | 7.6 | 7.6 | 7.6 | N/A | N/A |
Adaptive via SA, | 8.3 | 8.0 | 7.2 | N/A | N/A |
Adaptive via IF, | 9.4 | 7.4 | N/A | N/A | N/A |
Adaptive via ES, | N/A | N/A | N/A | 7.6 | 6.9 |
2.84 Tbps | | | | | | |
Fixed via SA, | 11.3 | 11.3 | 11.3 | N/A | N/A |
Fixed via SA, | 12.7 | 12.0 | 11.2 | N/A | N/A |
Adaptive via SA, | 11.0 | 11.0 | 11.0 | N/A | N/A |
Adaptive via SA, | 11.8 | 11.6 | 10.8 | N/A | N/A |
Adaptive via IF, | 12.9 | 10.5 | N/A | N/A | N/A |
Adaptive via ES, | N/A | N/A | N/A | 10.8 | 10.4 |
Table VI
Spectrum Utilization for 8-Node Network With Static Traffic
Load | Algorithm | Average Spectrum Utilization (%) |
---|
2 Tbps | | | | | |
Fixed via SA, | 13.5 | 13.5 | 13.5 | 13.5 |
Fixed via SA, | 14.5 | 13.9 | 13.4 | 12.5 |
Fixed via SA, | 15.3 | 15.0 | 13.9 | 12.9 |
Adaptive via SA, | 12.8 | 12.8 | 12.8 | 12.8 |
Adaptive via SA, | 13.9 | 13.5 | 12.5 | 12.0 |
Adaptive via SA, | 15.3 | 14.2 | 13.9 | 12.7 |
Adaptive via IF, | 16.7 | 12.5 | 11.1 | N/A |
15 Tbps | | | | | |
Fixed via SA, | 41.4 | 41.4 | 41.4 | 41.4 |
Fixed via SA, | 44.4 | 43.1 | 41.2 | 37.5 |
Fixed via SA, | 48.6 | 47.2 | 45.8 | 40.3 |
Adaptive via SA, | 30.9 | 30.9 | 30.9 | 30.9 |
Adaptive via SA, | 33.3 | 31.9 | 30.6 | 29.2 |
Adaptive via SA, | 41.7 | 37.5 | 36.1 | 32.9 |
| Adaptive via IF, | 34.7 | 30.6 | 27.8 | N/A |
Table VII
Spectrum Utilization for 8-Node Network With Dynamic Traffic
Load | Algorithm | Average Spectrum Utilization (%) |
---|
3.35 Tbps | | | | | |
Fixed via SA, | 18.3 | 18.3 | 18.3 | 18.3 |
Fixed via SA, | 19.4 | 18.5 | 18.0 | 16.7 |
Fixed via SA, | 20.8 | 19.4 | 18.3 | 17.1 |
Adaptive via SA, | 16.8 | 16.8 | 16.8 | 16.8 |
Adaptive via SA, | 18.1 | 16.7 | 16.3 | 15.7 |
Adaptive via SA, | 18.8 | 17.7 | 16.9 | 15.9 |
Adaptive via IF, | 19.4 | 16.7 | 15.3 | N/A |
12.53 Tbps | | | | | |
Fixed via SA, | 44.4 | 44.4 | 44.4 | 44.4 |
Fixed via SA, | 48.6 | 46.8 | 44.4 | 40.3 |
Fixed via SA, | 52.8 | 50.0 | 48.6 | 45.8 |
Adaptive via SA, | 34.7 | 34.7 | 34.7 | 34.7 |
Adaptive via SA, | 37.5 | 36.1 | 34.9 | 33.5 |
Adaptive via SA, | 40.3 | 38.9 | 37.5 | 36 |
Adaptive via IF, | 33.7 | 31.3 | 27.1 | N/A |
Table VIII
Spectrum Utilization for NSFNet Network With Static Traffic
Load | Algorithm | Average Spectrum Utilization (%) |
---|
4 Tbps | | | | | | | |
Fixed via SA, | 13.5 | 13.5 | 13.5 | 13.5 | 13.5 | 13.5 |
Fixed via SA, | 14.8 | 14.2 | 13.6 | 13.4 | 13.4 | 12.5 |
Fixed via SA, | 14.9 | 14.4 | 13.9 | 13.6 | 13.5 | 13.1 |
Fixed via SA, | 16.5 | 15.9 | 15.3 | 15.0 | 14.8 | 13.6 |
Fixed via SA, | 16.8 | 15.9 | 15.5 | 15.3 | 14.8 | 14.2 |
Adaptive via SA, | 13.0 | 13.0 | 13.0 | 13.0 | 13.0 | 13.0 |
Adaptive via SA, | 13.6 | 13.4 | 13.3 | 13.1 | 13.1 | 11.9 |
Adaptive via SA, | 13.5 | 13.4 | 13.1 | 12.8 | 12.6 | 12.4 |
Adaptive via SA, | 14.8 | 14.2 | 13.9 | 13.6 | 13.3 | 12.9 |
Adaptive via SA, | 14.6 | 14.3 | 13.9 | 13.7 | 13.6 | 13.0 |
Adaptive via IF, | 14.2 | 12.5 | 12.4 | 12.4 | 12.5 | N/A |
15 Tbps | | | | | | | |
Fixed via SA, | 32.2 | 32.2 | 32.2 | 32.2 | 32.2 | 32.2 |
Fixed via SA, | 36.4 | 35.2 | 33.9 | 32.4 | 31.8 | 31.3 |
Fixed via SA, | 38.6 | 37.5 | 35.8 | 34.1 | 33.5 | 31.9 |
Fixed via SA, | 39.8 | 38.6 | 38.0 | 36.9 | 35.8 | 34.7 |
Fixed via SA, | 40.2 | 39.1 | 38.6 | 37.9 | 37.2 | 35.8 |
Adaptive via SA, | 25.9 | 25.9 | 25.9 | 25.9 | 25.9 | 25.9 |
Adaptive via SA, | 27.5 | 27.3 | 26.7 | 26.0 | 25.6 | 24.4 |
Adaptive via SA, | 30.7 | 30.1 | 28.4 | 27.8 | 27.5 | 26.1 |
Adaptive via SA, | 31.8 | 31.3 | 31.0 | 30.7 | 30.4 | 29.0 |
Adaptive via SA, | 33.5 | 33.0 | 32.4 | 31.8 | 31.3 | 30.0 |
Adaptive via IF, | 27.8 | 23.9 | 25.6 | 23.3 | 23.3 | N/A |
Table IX
Spectrum Utilization for NSFNet Network With Dynamic Traffic
Load | Algorithm | Average Spectrum Utilization (%) |
---|
4.98 Tbps | | | | | | | |
Fixed via SA, | 15.0 | 15.0 | 15.0 | 15.0 | 15.0 | 15.0 |
Fixed via SA, | 16.5 | 15.9 | 15.7 | 15.3 | 14.8 | 14.2 |
Fixed via SA, | 18.8 | 18.2 | 17.6 | 17.1 | 16.5 | 15.3 |
Fixed via SA, | 18.9 | 18.6 | 18.2 | 18.0 | 17.8 | 17.1 |
Fixed via SA, | 19.3 | 19.0 | 18.7 | 18.5 | 18.2 | 17.6 |
Adaptive via SA, | 14.2 | 14.2 | 14.2 | 14.2 | 14.2 | 14.2 |
Adaptive via SA, | 14.8 | 14.6 | 14.4 | 14.3 | 13.9 | 13.2 |
Adaptive via SA, | 15.8 | 15.6 | 15.4 | 14.9 | 14.8 | 14.2 |
Adaptive via SA, | 16.5 | 16.2 | 15.8 | 15.5 | 15.2 | 14.5 |
Adaptive via SA, | 16.9 | 16.7 | 16.3 | 15.9 | 15.5 | 15.0 |
Adaptive via IF, | 16.5 | 14.2 | 13.6 | 13.6 | 13.6 | N/A |
12.12 Tbps | | | | | | | |
Fixed via SA, | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 |
Fixed via SA, | 29.0 | 28.4 | 27.9 | 27.3 | 26.9 | 25.6 |
Fixed via SA, | 31.8 | 31.3 | 30.7 | 30.3 | 29.9 | 29.0 |
Fixed via SA, | 32.8 | 32.4 | 32.1 | 31.8 | 31.2 | 30.7 |
Fixed via SA, | 33.2 | 32.9 | 32.6 | 32.4 | 31.9 | 31.2 |
Adaptive via SA, | 23.3 | 23.3 | 23.3 | 23.3 | 23.3 | 23.3 |
Adaptive via SA, | 23.9 | 23.3 | 22.9 | 22.6 | 22.2 | 20.8 |
Adaptive via SA, | 25.6 | 25.2 | 24.8 | 24.3 | 23.9 | 23.0 |
Adaptive via SA, | 28.4 | 27.9 | 27.3 | 26.6 | 25.8 | 24.4 |
Adaptive via SA, | 30.0 | 29.1 | 28.5 | 27.9 | 27.3 | 26.2 |
Adaptive via IF, | 23.3 | 20.5 | 19.8 | 20.5 | 19.9 | N/A |