Ring networks are suited to deliver a large amount of bandwidth in a reliable and inexpensive way. An optimal load balancing is of paramount importance because it increases the system capacity and improves the overall ring performance. In this context an important optimization problem is the Weighted Ring Loading Problem. That is the design of a direct path for each request, in a communication network, in a way that high load on the arcs/edges will be avoided, where an arc is an edge endowed with a direction. We study two variants of this problem without demand splitting. The work presented...