Abstract: A novel problem of maximizing throughput of requests was studied on the ring network in SONET,i.e.,let R be a ring on vertices 0,1,…,n-1 in SONET,each edge ei=(i,i+1) contains its integer capacity di and there exist m pairs of requests si,ti(1≤i≤m and si≠ti).The objective of this problem was to route some (maybe all) of these m requests so as to maximize the number of the different paths used,each connecting si and ti and satisfying the amount of paths through each edge is not beyond its integer capacity of that edge. By using the concept of one-direction and the technique of LP-rounding, the problem of ring with one direction was proved to be in P,i.e.,there exists a polynomially optimal algorithm that can solves it.Moreover,a 2-approximation algorithm to this problem in ring network was given thereby.