An ATM switch based on multistage interconnection networks with multiple paths can support higher bandwidth than that of buffered networks with single path by passing multiple packets to the same destination simultaneously. These multiple packets are buffered in the output buffer of the destination. The performance of output buffer in the switch with multiple paths is closely dependent on the output traffic distribution, which is the packet arrival rate at each output link destined to a given output port. As the nonuniformity of the output traffic distribution becomes higher, the performance of the output buffer as like delay and packet loss probability gets better. In this paper, we propose a new self-routing switch architecture with multiple paths called Fly network and analyze the performance of the switching network and the output buffer focusing on the output traffic distribution. It is shown that the Fly network supports best throughput and latency of the output buffer by producing a high degree of the nonuniform output traffic distribution