Communications networks with multiple parallel channels become more feasible more than before because of the decreasing cost of equipments. Advantages of using multiple parallel channels to connect terminals include better reliability and fault‐tolerance capability, higher throughput and lower delay, easier implementing priority schemes, and more adaptable to provide various kinds of network services. We analyze in this paper the performances of four different channel selection methods in a network with multiple parallel channels. The basic idea is that the performance can be significantly improved by transmitting multiple copies of the same packet simultaneously. We also evaluate the performance deterioration caused by channel failures. The deterioration is observed to be significant if users do not know which channels are out of order. However, an efficient fault‐diagnosis technique is very helpful to alleviate the deterioration. Some easily implementable priority schemes, which are called priority by diversity, priority by privilege, and priority by diversity and privilege, are discussed and evaluated. By appropriately adjustig the values of the control parameters, one can get a suitable priority scheme to achieve the desired performance.