We consider a standard splitting algorithm for the rare-event simulation of
overflow probabilities in any subset of stations in a Jackson network at level
n, starting at a fixed initial position. It was shown in DeanDup09 that a
subsolution to the Isaacs equation guarantees that a subexponential number of
function evaluations (in n) suffice to estimate such overflow probabilities
within a given relative accuracy. Our analysis here shows that in fact
O(n^{2{\beta}+1}) function evaluations suffice to achieve a given relative
precision, where {\beta} is the number of bottleneck stations in the network.
This is the first rigorous analysis that allows to favorably compare splitting
against directly computing the overflow probability of interest, which can be
evaluated by solving a linear system of equations with O(n^{d}) variables.