# TFBN: A Cost Effective High Performance Hierarchical Interconnection Network
## 5 Static Cost Effectiveness Analysis of a TFBN
### Cost Effective Factor  
A massively parallel computer system is constructed by connecting numerous nodes interconnected using communication links under an interconnection network topology. The major cost of a node is incurred because of its processing elements, router, and memory. Considering the price of communication links or cables in creating an MPC system is also one of the important factors to calculate the actual cost of an MPC system. The price of the wires has a crucial influence on the cost of building MPC systems; therefore, finding a new parameter using the cost of these wires to evaluate these systems is important.  
Usually, the parallel computer system is used to reduce the processing time and speed up the operation. The evaluation of the performance of MPC systems takes into account speedup and efficiency to assess these systems. The more nodes that are interconnected together, the more speed that will be attained. In addition, surely the ratio is not linear. The speedup and thus the efficiency of an MPC system depend on the proficient use of the communication links used to interconnect the MPC system.  
The cost-effective factor (CEF) is considered as a crucial static parameter to assess the feasibility of an MPC system. This parameter considers the cables count as a function of the processors' count. Therefore, it denotes \(CEF(p,l)\), where \(p\) represents the number of processing elements or cores and \(l\) represents the number of links. The proportion of wires count to nodes count denoted as \(G(p)=(\mathit{Total\ \#\ of\ links})/(\mathit{Total\ \#\ of\ nodes})\). The cost of processing elements is represented as \(C_{p}\), and the cost of communication links is represented as \(C_{l}\). The parameter \(\rho\) is outlined as the ration between \(C_{l}\) and \(C_{p}\), and \(0\leq\rho\leq 1\). To evaluate the CEF parameter, we have considered the homogeneous parallel computer systems whereby the cost of processors and cables is maintained as a similar ration. Considering \(p\), \(l\), \(G(p)\), \(C_{p}\), and \(C_{l}\), and \(\rho\), the CEF of an interconnection network topology is expressed as the following Equation (2):  
\[CEF=\frac{1}{1+\rho\times G(p)} \tag{2}\]  
We have assessed time cost-effective factors of TFBN along with the TTN and TESH network, 2D-torus, and 2D-mesh networks for different \(\rho\) ranging from 0.1 to 1.0 and plotted in Figure 4. We have considered two different size networks such as 256 nodes and 4096 nodes. Figure 3(a) portrayed the CEF of different networks for 256 nodes and Figure 3(b) portrayed the same for 4096 nodes. For all the values of \(\rho\), (\(0.1\leq\rho\leq 1.0\)), the CEF of TFBN is substantially less than that of TTN, TESH, torus, and mesh networks. From \(\rho=0.3\)) and onward, the CEF of the TFBN is significantly lower than those networks for both 256 node and 4096 node networks. This proves that TFBN is a profitable network compared to these networks. This qualifies TFBN to be a good choice compared to many conventional and hierarchical interconnection networks to frame future generation supercomputers or MPC systems.