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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  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 2β+1 function evaluations suffice to achieve adoi:10.1214/11-ssy026 fatcat:dypdocszwvecrauubm32vzxevq