Simulation run length planning

Abstract

The standard statistical theory leading up to the large-sample formula for the required simulation run length with the relative width criterion is reviewed. Some of the reflecting Brownian motion (RBM)-type examples of W. Whitt (1989), including the M/M/1 queue, RBM, the GI/G/m queue, and a packet queue model, are discussed. The packet queue model is relatively complicated, so that an exact analysis is evidently not possible with the current methodology. However, simple formulas for determining appropriate simulation run lengths can be obtained from the RBM approximation. These examples show that it can be misleading to do an exploratory simulation with one set of parameter values to determine appropriate simulation run lengths because the appropriate run lengths are very different for different traffic intensities The asymptotic formulas for Markov processes are also reviewed, including explicit formulas for birth and death processes and diffusion processes.