  The paper establishes necessary and sufficient conditions for stability of
different join-the-shortest-queue models including load-balanced networks with
general input and output processes. It is shown, that the necessary and
sufficient condition for stability of load-balanced networks is associated with
the solution of a linear programming problem precisely formulated in the paper.
It is proved, that if the minimum of the objective function of that linear
programming problem is less than 1, then the associated load-balanced network
is stable.
