Analysis of a Finite Number of Deflections in Fully and Uniformly Loaded Regular Networks

This paper presents an analytical methodology to obtain steady state throughput of a uniformly and fully loaded regular network. The network operates using deflection routing under the condition that a data packet is allowed to experience a finite number of deflections. Unlike the published analytical methods, the proposed method allows the analysis of a final number of deflections a packet can experience by means of harnessing polynomials in a novel way. The analytical results of the network throughput agree with the simulation results with relative error of 1% on average. The analysis is presented in the context of the shufflenet with the node connectivity of two. The largest network considered in the article has 896 nodes.