Page 69 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1

Fig. 1 – Flow chart of proposed method.

topology as an undirected graph ( , ), where
denotes network switches and represents ibre links
(edges) connecting the switches. This is followed by
the extraction of the geographic location data using
the input data set. Next, the Harvesine approach is
applied on the location data to generate the distance
matrix. To determine edge weights, an adjacency matrix
is implemented between all connected switches. Then,
computation of the number of controllers that minimize
intra‑cluster latency is carried out using the Silhouette (a)
algorithm as described in Section 4.2.1, Algorithm 1.
To verify the results from Silhouette, Gap Statistics is
implemented as described in Section 4.2.2, Algorithm
2. This is followed by computation of the shortest
path matrix by applying Johnson’s algorithm outlined in
Algorithm 3. The results from Silhouette, Gap Statistics
and Johnson’s algorithm, are used as inputs to the
PAM algorithm discussed in Section 4.3.2, Algorithm 4,
which is used to ind the best locations that minimize
propagation latencies, namely the average latency and
worst‑case latency de ined in Section 4.3.2 (Eq (6) and
(7)). The key factor in our mathematical formulation (b)
is the distance (under the assumption of constant
bandwidth across all ibre links). Therefore under
constant bandwidth, propagation latency is directly
proportional to distance.

6. RESULTS FOR MATHEMATICAL
MODELLING

This section presents and discusses the results obtained
after applying the approaches described in Section 4.
(c)
6.1 Optimal number of controllers

Fig. 2 – Silhouette analysis to determine optimal number of controllers
6.1.1 Silhouette analysis for (a) = 2(b) = 3(c) = 4.
In order to determine the optimal number of controllers
to deploy on the SANReN backbone, we applied our These plots show the clustering quality when a different
enhanced Silhouette algorithm with propagation latency number of SDN controllers are deployed. For instance,
as our key performance indicator. The results from our Fig. 2 ( ) illustrates the clustering quality when 2
Silhouette analysis are as depicted in Fig. 2. controllers are deployed. The metric used to measure

© International Telecommunication Union, 2021 53