  In this paper we show that in a multiclass Markovian network with unit rate
servers, the condition that the average load $\rho$ at every server is less
than unity is indeed sufficient for the stability or positive recurrence for
\emph{any} work conserving scheduling policy and \emph{class-independent}
routing. We use a variation of the positive recurrence criterion for
multidimensional discrete-time Markov chains over countable state spaces due to
Rosberg (JAP, Vol.~17, No.~3, 1980) and a monotonicity argument to establish
this assertion.
