# Numerical Results and Analysis

Figures 7.5(a) and 7.5(b) show the blocking probabilities of the dedicated partition and non-partition approaches with different spectrum allocation policies, namely, first fit, random fit, first-last fit for NSFNET and the Indian network, respectively. It is evident from both figures that the dedicated partition approach with first-last fit spectrum allocation policy provides the lowest blocking probability. This is due to the dedicated partitioning approach and the first-last fit spectrum allocation policy. The dedicated partitioning approach provides more aligned available slots and the first-last fit spectrum allocation policy gives more contiguous available slots. As a result, the maximum number of lightpaths is established compared to other schemes. We can also observe that the dedicated partition approach with first fit spectrum allocation policy provides higher blocking probability than that of the non-partition approach with first fit spectrum allocation policy. This is because, the first fit spectrum allocation policy provides more

**Figure 7.5: **Blocking probability versus traffic volume, obtained by using different schemes for (a) NSFNET and (b) Indian network.

contiguous available slots without the partitioning approach. The non-partition approach with first fit spectrum allocation policy has more contiguous available slots than that of the non-partition approach with first-last fit spectrum allocation policy. In the non-partition approach with first-last fit spectrum allocation policy, the number of contiguous available slots is smaller than that of the nonpartition approach with first fit spectrum allocation policy as the available slots are squeezed in the middle of the subcarrier slots. Therefore, the blocking probability using the non-partition approach with first-last fit spectrum allocation policy is lower than that of using the non-partition approach with first fit spectrum allocation policy. The random fit spectrum allocation policy provides the worst performance in terms of the blocking probability compared to the other spectrum allocation policies. This is due to the random fit policy allocates slots randomly, and thus the number of contiguous available slots is reduced. The dedicated partition approach with random fit spectrum allocation policy allocates the slots randomly inside each partition and results in more aligned available slots compared to the non-partition approach with random fit spectrum allocation policy. This in turn leads to lower blocking probability compared to the non-partition approach with random fit spectrum allocation policy.

As we already mentioned that partitioning would be beneficial for reducing the blocking probability in elastic optical networks, provided the number of partitions is minimized. Therefore, the performance of the dedicated partition approach is evaluated in terms of the blocking probability as the number of partitions is reduced. The number of partitions in the dedicated partition approach is reduced with the consequence that not all lightpath groups assigned in the same partition are disjointed. Figure 7.6 shows the blocking probabilities of the dedicated partition approach under a different number of partitions and the non-partition approach with first fit spectrum allocation policy for NSFNET. We observe that when the number of partitions is two, the blocking probability is the lowest among other number of partitions. Therefore, we deduce that the reduction of the number of partitions could reduce the blocking probability.

Figure 7.7 plots the blocking probability versus traffic volume obtained by using different non-defragmentation approaches. For comparison, we incorporate the results of dedicated partition approach with two partitions. We observe that the pseudo partitioning approach provides the lowest blocking probability among all non-defragmentation approaches considered. This is because the separation of the disjoint and non-disjoint ligthpaths. This separation provides more aligned available slots thereby reducing the blocking probability in the network. Dedicated partitioning approach also separates the disjoint and non-disjoint ligthpaths. In dedicated partitioning, to avoid statistical multiplexing gain issue, we

**Figure **7.6: Blocking probability versus traffic volume under different number of partitions using partition scheme with first-last fit spectrum allocation for NSFNET.

**Figure **7.7: Comparison of blocking probabilities using different non-defragmentation approaches.

**Figure 7.8: **Comparison of contiguous-aligned available slot ratios using different nondefragmentation approaches.

reduce the number of partitions by violating the disjoint constraint, and hence it provides more fragmented slots compared to the pseudo partitioning approach. We noticed, but did not include in the figure, that the multipath routing approach yields lower blocking probability than the traditional routing and spectrum allocation approaches. This is because the multipath routing approach splits bandwidth requests into different parts and transfers these parts along one or more lightpaths by utilizing sliceable bandwidth variable transponders. We noticed that the pseudo partitioning approach offers higher contiguous-aligned available slot ratios than the other non-defragmentation approaches considered, which is captured in Fig. 7.8.

In summary, we observed that non-defragmentation approaches suppress the probability of blocking due to bandwidth fragmentation. Among different non-defragmentation approaches considered, the pseudo partitioning approach outperforms the non-defragmentation approaches. As non-defragmentation approaches have lower performance in terms of blocking probability than the de- fragmentation approaches, the next chapter (Chapter 8) will discuss different de- fragmentation approaches.

**Exercises**

- 1. Why is pseudo partitioning better than dedicated partitioning?
- 2. Calculate the blocking probability of a fiber link using Erlang В loss formula under the following conditions:

i Lightpath requests arrive in the system based on a Poisson arrival process and their holding times follow an exponential distribution.

ii The number of channels is 120 and the offered traffic is 100 Erlang.

- 3. Estimate the blocking probability of each partition when 120 channels of a fiber link are divided among 10 partitions and splitting the traffic (100 Erlang) among the partitions (i.e., 12 channels with offered traffic volume of 10 Erlang); the traffic assumption remains the same with Exercise 2.
- 4. Why does the separation of disjoint and non-disjoint requests have better impact in terms of fragmentation in the partitioning approach over without separation of requests?
- 5. Why is the first-last fit spectrum allocation more suitable for pseudo partitioning in terms of blocking ratio over the first fit policy.
- 6. Discuss the negative aspects of spectrum split routing.
- 7. Estimate average slot utilization under the following conditions.

i Average number of route hops is four.

ii Traffic load in the network is 100 Erlang.

iii The network contains 20 links and each link contains 10 slots.

8. What is confidence interval and what does margin of error indicate?

**Chapter 8**