Individually and overall optimal routing problems are considered for networks with nodes interconnectedby a generally configured manner and with multiple classes of users. The two problemsare formulated along with the discussions on mutual equivalence between both problems, on theexistence and uniqueness of solutions, and on the relation between the formulations with path andlink flow patterns. We show that a link-traffic loop-free property holds within each class for bothindividually and overall optimal routing in a wide range of networks, and show the condition thatcharacterizes the category of networks for which the property holds.
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