In this paper, we investigate the performance characteristics of parallel switching architectures constructed by a stack of multistage switching networks. First, we propose a general analysis model which describes two directional traffic flows with a traffic-distribution characteristic. By applying this model to an MBCP (multiple banyan connected in parallel) switch, we show that the traffic-distribution characteristic plays an important role for the accuracy of a performance model. Next, to verify the accuracy of our approach to model the parallel switching architecture with a traffic-distribution capability, we select and analyze the WGSN (weaved generalized shuffle network) which is based on a multihop switching architecture. From the comparison with simulation results, we show that the developed model accurately predicts the performance of a WGSN under the assumption that the traffic-distribution characteristic is uniform.