Banyan networks and their improved switches such as 2-dilated banyan networks are usually constructed by a self-routing mechanism, and provide a high multiplexing transmission capacity to ATM networks. Due to cell blocking in the switching elements in these banyan networks, however, cell loss is occurred and then the throughput of each network is decreased. To improve this problem, we have introduced bypasses to the original and the 2-dilated banyan networks. This paper focuses on the position of the bypasses in these banyan networks and proposes the one-bypass-connection methods in order to minimize cell transfer delay caused by the bypasses. We also analyze output rate of each network and show that the bypass method gives network designers flexible selections for network performance and transfer delay.

Most of the existing analytical models for multistage ATM switching fabric are not accurate in the presence of a non-uniform traffic at the input of the switch. In this paper, we discuss the issues in modeling a multistage ATM switching fabric, and investigate the effect of independence assumptions in two previous analytical models. A highly accurate 4-state Markov chain model for evaluating the performance of ATM switching fabrics based on multistage switches with 22 finite output-buffered SEs is proposed. The proposed model correctly reflects the correlation of cell movements between two subsequent cycles and states of the buffers of two adjacent stages. By comparing the results obtained from the oroposed model, existing models and simulations, it has been shown that the proposed model is much more accurate than existing models in the presence of a non-uniform traffic in the switch. The results from the existing models are unsatisfactory in the presence of an increased blocking in the switch arising from a non-uniform traffic in the switch. On the contrary, the proposed model is very robust even under severe blocking in the switch.