Although high-speed multi-plane switching networks have removed their internal conflict problem, a routing control algorithm is necessary for realizing conflict-free routing. Otherwise, the conflict phenomenon cannot be totally avoided. This is because the routing plane may be chosen inappropriately by the incoming packet at the input stage. Therefore, a control algorithm based on the idea of conflict links set is presented in this paper. This algorithm controls the allocation of packets among routing planes in the multi-log₂N switching networks, and hence, the conflict-free routing is totally guaranteed. Moreover, it is not only applicable for the RNB and SNB, but also suitable for unicast and multicast. On the other hand, inner link conflicts are removed in multi-log₂N networks. The switching efficiency is improved, but no performance analysis models can be used to analyze the switching performance of Multi-log₂N switching networks. So an analysis model based on embedded Markov chain is proposed in this paper, and is adopted to analyze the queue management and the relevant performance measures in detail, such as the mean waiting time, queue length and the probability of packets loss. All these conclusions are capable of providing well theoretical support for the design of the optical switching architecture based on multi-log₂N switching networks.