Havihg modified and extended the routing algorithm used in our previously proposed Bidirectional Shuffle Ring Network (BSRN), we here provide some adaptive routing algorithms that can relieve the congestion caused by bottlenecks when nonuniform traffic exists. As to preserve the transmission order of cells associated with a message which may otherwise arrive at the destination out of sequence if they are forwarded along different routing paths, two control schemes are also devised. The BSRN proves to be highly reliable and robust since countermeasures against node or link failure can also easily be realized.