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A theoretical model of an n-dimensional toroidal interconnection network with the virtual cut-through routing is developed. Network performance is characterized as a function of the message load for various values of the network and communication parameters. An exact analytical expression for the saturation point has been obtained. Latency as a function of message generation rate under the mean field theory approximation has been derived. The analysis is based on a Markov chain description of the routing queueing system. The saturation point has been found proportional to the number of the torus dimensions and inversely proportional to the message length and to the length of the path from the source to the destination. It was found that the transition to the saturation state is a second-order (continuous) phase transition with a critical exponent equal to 1. Simulation results show very good agreement with the theoretical analysis.

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Analysis and Simulation of Multidimensional Interconnection Networks with Virtual-Cut-Through Routing

  • 会议论文

  • 发表日期：

    2025年

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  • Benjamin Ehrlich,
  • Yelena Rykalova,
  • Lev B. Levitin

摘要

A theoretical model of an n-dimensional toroidal interconnection network with the virtual cut-through routing is developed. Network performance is characterized as a function of the message load for various values of the network and communication parameters. An exact analytical expression for the saturation point has been obtained. Latency as a function of message generation rate under the mean field theory approximation has been derived. The analysis is based on a Markov chain description of the routing queueing system. The saturation point has been found proportional to the number of the torus dimensions and inversely proportional to the message length and to the length of the path from the source to the destination. It was found that the transition to the saturation state is a second-order (continuous) phase transition with a critical exponent equal to 1. Simulation results show very good agreement with the theoretical analysis.