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