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Designing a Novel Star Topology using Operad Linear Differential Theory

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Abstract

In general, topology design is the most important framework in network communication. In this research, a star topology is adapted as an application. Normally, the star topologies are freely connected to the closed-loop systems and effectively created for all network applications. However, the failure of the central node leads to function error and system collapse. Once the network system gets collapsed then attaining the original states becomes difficult. To overcome this problem, a novel star topology is designed using the operad linear differential theory. This proposed mathematical star design efficiently reconstructs the network, when the collapse occurs. Moreover, the linear differential theory is mostly used to create a pertinent computational replica, and operad is perturbed with ideal algebras including associative and commutative properties. Furthermore, the proposed star topology design is applicable for Storage Area Network (SAN). Henceforth, the stability of the proposed method is determined using proper eigenvalues with specific theorems and conditions. The implementation of this research is done in the MATLAB platform. Thus, the proposed differential star topology is validated in the SAN application for data transmission. Besides, the proposed model is validated with other existing models using different key metrics to make the comparison assessment. Finally, the comparison results proved that the proposed linear differential theory is sufficient to be applied for SAN application with different network conditions.

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Notes

  1. Linear polynomial is defined as any polynomial equation in the form of \(q(x) = mx + n\), where \(m\) and \(n\) represented as real numbers.

  2. Taylor series is referred to as a sequence extension of a purpose regarding a point.

  3. Diagnosable means, it estimates the identity of real numbers whether it is equal to zero or less than zero.

  4. The critical point is the function of a solo real variable is \(f(x)\) is not differential in the domain of \(x_{0}\) or zero at its derivatives.

  5. Here in the network topology, the hub is derived by the critical points of differential star node strategy.

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Authors and Affiliations

  1. Department of Mathematics, University College of Engineering, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirapalli, Tamil Nadu, 620 024, India

    Kalaiselvi Sundaram

  2. Department of Mathematics, University College of Engineering Panruti (UCEP), Panruti, Tamil Nadu, 607 106, India

    Seenivasan Vellupillai

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Correspondence to Kalaiselvi Sundaram.

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Sundaram, K., Vellupillai, S. Designing a Novel Star Topology using Operad Linear Differential Theory. Wireless Pers Commun 120, 565–585 (2021). https://doi.org/10.1007/s11277-021-08478-0

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