A family of bijections between G-parking functions and spanning trees

For a directed graph G on vertices {0,1,…,n}, a G-parking function is an n-tuple (b1,…,bn) of non-negative integers such that, for every non-empty subset U⊆{1,…,n}, there exists a vertex j∈U for which there are more than bj edges going from j to G-U. We construct a family of bijective maps between the set PG of G-parking functions and the set TG of spanning trees of G rooted at 0, thus providing a combinatorial proof of |PG|=|TG|.