Stochastic simulation models are used to predict the behavior of real systems whose components have random variation. The simulation model generates artificial random quantities based on the nature of the random variation in the real system. Very often, the probability distributions occurring in the real systems are unknown, and must be estimated using finite samples. This paper presents two ways to estimate simulation model output errors due to the errors in the empirical distributions used to drive the simulation. These approaches are applied to simulations of the M/M/1 queue with an empirically sampled interarrival time. They capture components of variance in the estimate of mean time in the system that are ignored when the empirical distribution is treated as the true distribution.