# Static Evaluation of a Midimew Connected Torus Network for Next Generation Supercomputers
## 1 Introduction
For example, AI applications rely on supercomputers for complex modeling tasks, such as seismic imaging, climate/environmental geospatial predictions, and computational astronomy [27]. Therefore, supercomputers have been shown to be ideal for training deep neural networks (DNNs) by processing the large datasets required for fast and accurate DNN results [28; 29]. Supercomputers have been linked directly to grand challenges and their solutions [30]. Therefore, many research centers are rapidly adopting supercomputer resources due to these benefits. In this paper, we addressed a serious concern in the implementation of supercomputers, which is the topology connecting massive numbers of nodes. This topology directly impacts the performance of MPCs [31]. Therefore, hierarchical interconnection networks (HINs) have received much attention from the research community. HINs enable the connection of large numbers of nodes with reasonable delays, as compared to conventional networks [32]. Supercomputer connections have reached the capacity of one million nodes, making conventional networks infeasible [33]. In our previous work, we proposed an HIN called an MTN, which used 2D torus connected by midimew links to build higher levels in order to include greater numbers of nodes [31]. However, the current research aimed to evaluate the network topology represented by static parameters and cost effectiveness. The evaluation of topological properties is crucial for a hierarchal network to be considered for further development. MTNs provide optimal features for static and cost-effective performance. This is shown in a comparative analysis of static network performance and cost-effective parameters according to the diameter and average distance evaluated by computer simulation. MTNs are compared to six other networks, two with conventional topologies, including 2D mesh and 2D torus. The presence of conventional networks in the evaluation was because of their current usage by supercomputers [34]. In addition, an MTN is compared to other HINs, including a midimew-connected mesh network (MMN) [35], a tori-connected mesh network (TESH) [36], a tori-connected flattened butterfly network (TFBN) [37], and a tori-connected torus network (TTN) [38]. The results of the simulated MTN showed a similar diameter to MMN that was lower than the mesh and TESH but higher than the other networks. MTNs have a lower average distance than almost all networks; a node degree which is lower than TFBN but higher than conventional networks; moderate bisection width; high arc connectivity; and higher costs as a result of wire complexity. However, MTNs also have better fault tolerance and bandwidth availability. In addition, in terms of static performance, MTNs have advantages in CPTFs, moderate time-cost-effective factors (TCEFs), message traffic density (MTD), and low packing density. However, MTNs have higher costs when compared to other networks, although they are still lower than mesh networks. This is a result of their improved bandwidth availability and high fault tolerance. Therefore, practical implementations of MPCs should consider adopting the most relevant features for the intended system. For example, high fault handling and sufficient bandwidth may make an MTN ideal for certain applications; however, considering its static performance and overall costs are worthy considerations. The remaining sections are organized as follows: Section 2 illustrates MTN architecture, followed by Section 3, which discusses the routing algorithm. Section 4 provides a comparative analysis of the static network performance. Section 5 shows the cost-effective analysis of the network. Finally, Section 6 presents the main findings and recommendations.