Since users on a network select paths so as to reach their destinations from their origins,
we consider variational inequality (32) as the basic one for the dynamical system equivalence.
Specifically, we note that, in view of constraint (28), one may define λˆ(x) ≡ λ(d), in which
case we may rewrite variational inequality (32) in the path flow variables x only, that is, we
seek to determine x∗ ∈ RnP
+ , such that