Let Pω denote the set of paths conn

Let Pω denote the set of paths connecting the origin/destination (O/D) pair of nodes
ω. Let P denote the set of all paths in the network and assume that there are J origin/destination
pairs of nodes in the set Ω. Let xp represent the nonnegative flow on path
p and let fa denote the flow on link a. The path flows on the network are grouped into the
column vector x ∈ RnP
+ , where nP denotes the number of paths in the network. The link
flows, in turn, are grouped into the column vector f ∈ RnL
+ , where nL denotes the number
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of links in the network.