Algorithm 1 Optimization problem solution for the tree network.

Create tree object T with system parameter values

for (k = T .BreadthTrav)! = null do {traverses T, returns a pointer to current node}

if k is a Leaf node then

Jk = 0, rk = 0

continue

end if

for (V=Tk .ChildTrav)!= null do {traverses child nodes, breadth-first, returns a pointer to current node}

C = [C Cv ], J = [J Jv ], r = [r rv ]

end for

OptFunc(k, J, C, r, q, R, Jk, rk) {call optimization algorithm for Equation (34)}

end for