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This tab could be used to generates a topology or just create matrices for a given topology such as distance, bandwidth and load matrices. Therefore, it is very useful to produce or modify test topologies in order to examine them and analyse their behaviour in the different status. The use of this generator is displayed below with its figures.

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A) Generating a new topology: this tab has two different topology generators. Every

topology generator has a different method to generate a topology (see Figures 5.6 and 5.7).

1) Generator-one, creates a network in which its nodes are connected in a completely

random manner, as shown in Figure 5.6. This generator produces a network which could join the first node with the last node because it does not provide any control over its randomisation of the connectivity. This generator is good for building large-sized network, but its networks extend in just about in all directions equally.

 Using the Generator-one

 Chose Topology Generator 1 button.  Enter the Edge ratio

 _{Enter Nodes No.}

 _{Select Max. Degree and Min. Degree of graph nodes.}

 Select Bandwidth and Distance Check-Box if their matrices are required.  Select Load Check-Box if its matrix is required.

 _{Press Create Topology button.}

Page | 111  The work of Generator-one

 It starts by reading the number of nodes and edge ratio from the entered parameters. Then, it calculates the number of graph edges according to the following equation:

𝑵𝒐. 𝑬𝒅𝒈𝒆𝒔 = 𝒏 × 𝑴𝒂𝒙. 𝑫𝒆𝒈𝒓𝒆𝒆 𝟐 × 𝑬𝒅𝒈𝒆𝒔 𝒓𝒂𝒕𝒊𝒐 (5.1)  It uses the uniform distribution function to distribute the edges between the

nodes of the network. The distributed function of the generator-one formulates as follows:

𝒇 𝒏 = 𝟏

𝑴𝒂𝒙. 𝑫𝒆𝒈𝒓𝒆𝒆 − 𝑴𝒊𝒏. 𝑫𝒆𝒈𝒓𝒆𝒆 , ∀ 𝑛 ∈ 𝑁 5.2  It creates the selected matrices for the topology as will be explained in point (B).  It plots the topology.

2) Generator-two, creates a network while providing some control over the

connectivity randomisation in order to prevent the joining of the very far away nodes would produce a longitudinal network (see Figure 5.7 below).

Page | 112  Using the Generator-two

 Chose Topology Generator 2 button.

 Select the Scale to specify the connecting space.  Enter Nodes No.

 _{Select Max. Degree and Min. Degree of graph nodes.}

 Select Bandwidth and Distance Check-Box if their matrices are required.  Select Load Check-Box if its matrix is required.

 _{Press Create Topology button.}  The work of Generator-two

 _{It begins by reading the Nodes No. and a Scale value.}

 It computes the allowed searching space which could be used to find the next nodes that should be connected to the current node, according to the Equation 5.3.

𝑺𝒆𝒂𝒓𝒄𝒉 𝑺𝒑𝒂𝒄𝒆 = 𝑺𝒄𝒂𝒍𝒆 × 𝑴𝒂𝒙. 𝑫𝒆𝒈𝒓𝒆𝒆 (5.3)

 It uses the same uniform distributed function to distribute the edges onto the graph nodes (see Equation 5.2), but here, the node is only connected onto other nodes in the restricted search space, which is identified above.

 _{It creates the selected matrices for the topology as will be explained in point (B).}  It plots the topology.

Finally, it is worth noting that the colour-bar indicates the degree of the node in the graph.

B) Creating matrices: Additionally, this tab can create the distances and the bandwidth

of the link for an existing topology. Also, it can produce the load matrix for network switches.

1) Creating the distance matrix: the distance matrix is important to examine the

implementation of the controller placement algorithm. Therefore, this tab can establish a distance matrix in different ranges of distances (see Figure 5.8).

 _{Using the tab to create the distance matrix}

 _{Enter the name of the connectivity file (adjacency matrix of graph connectivity).}  Select the Bandwidth and Distance check-box.

 Enter the value in the Distance-Factor field to scale up or down the distances.  Press the button of Create Matrices.

 To display the bandwidths on the graph, only choose Distance-button that located in the plot showing the panel under the graph.

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 _{The working steps to create the distance matrix}

 _{Compute the betweenness centrality (bc) for all nodes of a network according} to the following equation (Matlab, 2017):

𝑏𝑐 𝑛 = 𝑁𝑜. 𝑆𝑕𝑝𝑠,𝑑(𝑛) 𝑁𝑜. 𝑆𝑕𝑝_𝑠,𝑑 𝑠,𝑑 ≠𝑛 (5.4) 𝑊𝑕𝑒𝑟𝑒 𝑛, 𝑠, 𝑑 ∈ 𝑁, 𝑠: 𝑠𝑜𝑢𝑟𝑐𝑒 𝑛𝑜𝑑𝑒, 𝑑: 𝑑𝑖𝑠𝑡𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑛𝑜𝑑𝑒, 𝑁𝑜. 𝑆𝑕𝑝𝑠,𝑑 𝑛 : 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑕𝑜𝑟𝑡𝑒𝑠𝑡 𝑝𝑎𝑡𝑕𝑠 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠 𝑎𝑛𝑑 𝑑𝑡𝑕𝑎𝑡 𝑝𝑎𝑠𝑠 𝑖𝑛 𝑛𝑜𝑑𝑒 𝑛, 𝑁𝑜. 𝑆𝑕𝑝𝑠,𝑑: 𝑡𝑕𝑒 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑕𝑜𝑟𝑡𝑒𝑠𝑡 𝑝𝑎𝑡𝑕𝑠 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠 𝑎𝑛𝑑 𝑑.

 Divide the network nodes according to its bc into three groups (high, medium and low).

 Split the distance into three ranges (short, medium and long).

 For the nodes of high bc randomly find the distance from the first range, for the nodes of medium bc find the distance in second range and the low bc nodes use the third range.

 Amplify or diminish the distance using the Distance-Factor.

 The distances are between (1 to 20 km), which are the optimal lengths for SD- WAN links that could apply this algorithm. Also, the algorithm could achieve Figure 5.8: The fourth tab of COVN simulator (Topology Generator, Creating distance matrix).

Page | 114 good results for longer links, therefore Distance-Factor is set to scale up the length of optics fibre links. See the available length of optics fibre links in (Cisco, 2016).

2) Creating the bandwidth matrix: the bandwidth is generated using a simple method

(see Figure 5.9 below).

 Using the tab to create a bandwidth matrix

 _{Enter the name of the connectivity file (adjacency matrix of graph connectivity).}  Select the Bandwidth and Distance check-box.

 Press the button ‘Create Matrices’.

 _{Choose the Bandwidth-button which is located in the plot showing the panel} under the graph to only display the bandwidths on the graph.

 The working steps to create the bandwidth matrix

 Compute the betweenness centrality (bc) for all nodes of a network according to the Equation 5.4 above:

 Divide the network nodes according to its bc into three groups (high, medium and low).

 Split the bandwidth into three ranges (high, medium and low).

 _{For the nodes of high bc randomly find the bandwidth from the first range, for} the nodes of medium bc search bandwidth in the second range and the low bc nodes use the third range.

 The bandwidths are between (1 to 10 Gbit/s), which are the most used bandwidths for optics fibre links (Johnson, 2009).

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3) Creating the load matrix: the load matrix is needed to implement load balancing

when implementing the COVN algorithm, and can be created as follows (see Figure 5.10):

 Using the tab to create a load matrix

 _{Enter the name of the connectivity file (adjacency matrix of graph connectivity).}  _{Select the load check-box.}

 Enter the value in the Over-Load-Rate field to scale up or down the loads.  Press the button of Create Matrices.

 _{To display the load on the graph, choose the Load-button which is located in the} plot showing the panel under the graph.

 _{The working steps to create load matrix}

 _{Compute the betweens centrality (bc) for all nodes of a network according to the} Equation 5.4 above:

 _{Divide the network nodes according to its bc into three groups (high, medium} and low).

 _{Split the load into three ranges (high, medium and low).}

 _{For the nodes of high bc, randomly find the bandwidth from the first range, for} the nodes of medium bc, search bandwidth in the second range and the low bc nodes use the third range.

 _{Amplify or diminish the loads using the Over-Load-Rate.}

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