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Linear Algebraic Theory for Designing the Bus Topology to Enhance the Data Transmission Process

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Abstract

Bus topology performs a significant part for describing the data transfer from one end to another in a single direction, where one node performs as a source and another end performs as the destination. The complexity of utilizing the bus topology is if the cable in the network has an issue then the entire network will be shut down. Moreover, high network traffic will arise which decreases the network performance because all the information is transferred in a single cable. The bus topology issue is complex to enhance the normal process but mathematically it is simple to reconstruct the function. Therefore, in this research data transmission of the bus topology can be designed by a novel linear algebraic theory. Besides, the linear algebraic theory for bus topology is validated by the specific theorems and the rank of the matrix is estimated by the proper calculations. The proposed design of bus topology is created by the MATLAB platform. Moreover, the created bus topology is validated in the Local Area Network (LAN) application for data transmission. Consequently, the proposed theory is compared with the other conventional techniques and proven the reliability of the novel method. Besides, the proposed bus topology design in LAN is compared with other existing methods in terms of throughput, delay, and packet delivery ratio. Therefore the results proved that the proposed scheme can attain better performance than the other conventional techniques.

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Fig. 1
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Source to Destination through the proposed bus topology

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Data Availability

Enquiries about data availability should be directed to the authors.

Notes

  1. The two vector spaces have invertible linear transformation which is called an isomorphism.

  2. Augmented matrix is the matrix which is used for performing the similar row operations on every given matrix.

  3. This is the process of solving the linear equation that has been changed into row-echelon form.

  4. Hermitian matrix is the complex square matrix which is equal to the conjugate transpose.

  5. variational theorem states that the trial energy can be larger or equal to the true energy.

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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), 607 106, Panruti, Tamil Nadu, India

    Seenivasan Velupillai

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  1. Kalaiselvi Sundaram
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  2. Seenivasan Velupillai
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Correspondence to Kalaiselvi Sundaram.

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Sundaram, K., Velupillai, S. Linear Algebraic Theory for Designing the Bus Topology to Enhance the Data Transmission Process. Wireless Pers Commun 126, 401–420 (2022). https://doi.org/10.1007/s11277-022-09751-6

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