Percentage pattern of transceivers grouped by MTD
Fig. 7.5 reports the evolution of the average percentage of transceivers by 750km, 1,500km and 3,000km against traffic load. For each traffic load, such an average is defined as follows:
AVG(percentage) = percentage12+ percentage18+ percentage24 3
where percentagex is the percentage of a kind of transceiver (750km, 1500km or 3000km) in the quasi-optimal solution of the problem whose amount of regenerable sites is x. We did the linear regression (f (x) = a × x + b) on the set of average per- centage for each kind of transceiver (classified by MTD) and displayed the obtained a and b on the top right of Fig. 7.5.
0 20 40 60 80 100 957 1915 2872 3830 4787 5745 6702 7660 8617 9575 10533 11490 AVG(percentage) Traffic load transceiver of 3000kms (a=0.000,b=73.820) transceiver of 1500kms (a=0.000,b=22.855) transceiver of 750kms (a=0.000,b=3.275)
MTD Mean Standard Deviation
3000km [71.4-75.6] [0.7-2.0]
1500km [21.4-24.9] [0.3-2.0]
750km [02.8-04.8] [0.3-1.0]
Table 7.3: Statistics of the percentage average
Table 7.3 shows the mean and the standard deviation of the set of AVG(percentage) with different traffic load for each MTD.
It turns out that transceivers of 3000km takes the largest part in the quasi-optimal solution (∼73%), then transceiver of 1500km takes about 23% and the ones of 750km takes the smallest part (∼4%). This fact makes sense since it is obvious that using long distance transceivers reduces the need of regenerators.
Fig. 7.5 shows that traffic evolution has no significant impact on the average percentage distribution of the set of transceivers grouped by MTD since parameter a keeps being 0 despite traffic increase.
Percentage pattern of transceivers grouped by bit-rate
Fig. 7.6 is similar to Fig. 7.5, except that its transceivers are classified by bit-rate instead of MTD. We also fit the data with the linear regression (f (x) = a × x + b).
This figure shows clearly that transceivers of 10Gbps has the largest percent- age (>50%) while other kinds of transceivers (40Gbps and 100Gbps) takes the rest. Moreover, transceiver percentage of 10Gbps slowly decreases with the evolution of traffic load (a = −0.0015 < 0) while transceiver percentages of 40Gbps and 100Gbps increase (a = 0.0010 and a = 0.0006).
The increasing momentum of transceivers of 100Gbps (a = 0.0010) is higher than the one of transceivers of 40Gbps (a = 0.0006). It means, in comparison with the percentage of transceivers of 40Gbps, the percentage of transceivers of 100Gbps is increasing in accordance with traffic load increment. However, when the traffic load is relatively small, both percentages have a meaningless difference.
0 20 40 60 80 100 957 1915 2872 3830 4787 5745 6702 7660 8617 9575 10533 11490 AVG(percentage) Traffic load transceiver of 10Gbps (a=-0.0015,b=86.324) transceiver of 100Gbps (a=0.0010,b=5.711) transceiver of 40Gbps (a=0.0006,b=7.857)
Impact of constraint of maximum regenerable sites over transceiver dis- tribution (grouped by bit-rate)
Fig. 7.7 compares two extreme cases where maximum amount of regenerable sites are 12 and 24. The former case is when such an amount is half number of nodes while the latter case means that every node can be a regenerable site. In Fig. 7.7, the dash lines are for the 12 regenerable sites case while the solid lines are for the 24 regenerable sites case. Blue and red indicates transceiver of 10 Gbps and 100 Gbps, respectively. Obviously, in the case of maximum 12 regenerable sites, the optimal solution uses more transceivers of 100Gbps and less transceivers of 10Gbps than in the case of maximum 24 regenerable sites. It makes sense since the first case has fewer choices of node to deploy regenerators than the second case has. We conclude that when such a constraint gets stricter, the optimal design has to deploy more and more transceivers of high capacity (100Gbps).
Fig. 7.7 also confirms the trend of using less transceivers of 10Gbps and more of 100Gbps as the traffic load increases. The next paragraph makes a quantitative comparison about the impact of maximum regenerable sites on the deployment cost. Since we do not consider grooming, the number of transceivers of a specific bit-rate at the end nodes of working paths is constant; consequently we can pre-calculated their numbers. However, the number of transceivers that are deployed at intermediate nodes depends on the maximum number of regeneration sites.
Impact of constraint of maximum regenerable sites over the deployment cost (CAPEX)
The main idea of restricting the maximum number of regenerable sites is to gather regenerators to few sites in order to take advantage of sharing support devices, such as cooling systems. By that way, we can reduce the operating cost (OPEX). As shown in previous paragraphs, such a constraint results in requiring more 100Gbps and 40Gbps transceivers, in the other words, increasing the deployment cost (CAPEX).
Fig. 7.8 shows the dependency of the transceiver costs on the maximum available regenerable sites. E.g., the transceiver cost in the case of 24 regenerable sites over the one of 12 regenerable sites may vary from 21.4% to 50.3%.
0 20 40 60 80 100 957 1915 2872 3830 4787 5745 6702 7660 8617 9575 10533 11490 Percentage Traffic load Transceivers 10Gbps (12) Transceivers 100Gbps (12) Transceivers 10Gbps (24) Transceivers 100Gbps (24)
Fig. 7.7: Comparison of percentages of transceivers grouped by bit-rate that is made between the case of maximum 12 regenerable sites and of maximum 24 regenerable sites
5000 6000 7000 8000 9000 10000 11000 12000 13000 957 1915 2872 3830 4787 5745 6702 7660 8617 9575 10533 11490 Cost Traffic load ngen=12 ngen=18 ngen=24
7.6
Conclusion
We develop a decomposition method to solve the multi-rate design problem taking into account the constraint of maximum regenerable sites which, to the best of our knowledge, has not been considered in literature. We discover that the traffic evolu- tion has almost no impact on the percentage distribution of transceiver grouped by MTD. When we group transceivers by bit-rate, when the traffic grows we see the per- centage of 100Gbps transceivers increases fastest, then the one of 40Gbps transceiver, as opposed to the reduction of the percentage of 10Gbps. Those points could be hints to develop a high scalable heuristic for huge networks where such an extract method is intractable.
We study the restriction on maximum regenerable sites and see a huge impact on the deployment cost. For US-24 network, when reducing the number of regenerable sites from 24 to 12, we can see that the increase in deployment cost is between 21.4% and 50.3%. Based on such information, a network designer can make a appropriate compromise between OPEX and CAPEX.