  Melamed's theorem states that for a Jackson queuing network, the equilibrium
flow along a link follows Poisson distribution if and only if no customers can
travel along the link more than once. Barbour \& Brown~(1996) considered the
Poisson approximate version of Melamed's theorem by allowing the customers a
small probability $p$ of travelling along the link more than once. In this
paper, we prove that the customer flow process is a Poisson cluster process and
then establish a general approximate version of Melamed's theorem accommodating
all possible cases of $0\le p<1$.
