On a class of Banyan networks and tandem Banyan switching fabrics

This paper examines the operating characteristics of a class of tandem Banyan switching fabrics (TBSF's) built using bi-delta networks. We use the functional equivalence between bi-delta networks to induce an equivalence between TBSF's. A weaker form of equivalence guaranteeing identical performance under conditions of symmetric traffic is studied, and a sufficient condition for weak equivalence between functionally distinct TBSF's is established. These results hold for a variety of conflict resolution policies (CRP's) in addition to the one studied by Tobagi et al. (see IEEE J. Select. Areas Commun., vol.9, p.1173, 1991). Simulations indicate that a TBSF constructed by cascading omega networks, (or in fact any other TBSF in its weak equivalence class), performs better than the two TBSF's studied by Tobagi et al., and converges rapidly to a theoretical lower bound on the loss rate, in the region of interest. It is also shown that this loss rate is almost independent of the size of such a TBSF in the region of interest.<
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