Hitting time in an m/g/1 queue

We study the expected time for the work in an M/G/1 system to exceed the le vel x, given that it started out initially empty, and show that it can be e xpressed solely in terms of the Poisson arrival rate, the service time dist ribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.