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This paper considers the nonblocking conditions for a multirate logd(N,0,p) switching network at the connection level. The necessary and sufficient conditions for the discrete bandwidth model, as well as sufficient and, in particular cases, also necessary conditions for the continuous bandwidth model, were given. The results given for dn-1/2f0≥f1+1 in the discrete bandwidth model are the same as those proposed by Hwang et al. (2005); however, in this paper, these results were extended to other values of f0, f1, and d. In the continuous bandwidth model for B+b>1, the results given in this paper are also the same as those by Hwang et al. (2005); however, for B+b≤1, it was proved that a smaller number of vertically stacked logdN switching networks are needed

mathematical problems in engineering

The Strict-Sense Nonblocking Multirate<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>…

The Strict-Sense Nonblocking Multiratelogd(N,0,p)…