Toward guidelines for designing experiments in queuing simulation

Abstract

The simulation of complex queuing systems is an im portant application for discrete-event digital simula tion. In many cases, the object of the analysis is estimation of steady-state measures (e.g., mean and variance of waiting time) for the system. The initial conditions in the system at the start of a simulation run may introduce a "bias" into the experimental re sults; several methods have been suggested to eliminate this bias. One common approach is a warm-up period at the beginning of the simulation run, during which no data are collected. The length of this warm-up period is determined by a tradeoff between the reduction in bias caused by the initial conditions and the increase in variance of the statistical estimates resulting from discarding the initial data, given that the analyst is operating with a fixed experimental budget.

This paper explores the effect of initial conditions and the warm-up period on the design of simulation experiments for the simple case of a single-server queuing system with Poisson input and exponential service times. The experimental design problem is to determine the number of independent replications of a simulation run, the length of the warm-up period, and the length of the data-collection period, which together minimize the mean-square error of the estimated mean waiting time, subject to a budget constraint on the total number of customers whose progress through the system can be simulated. Optimal experiment design was found to be strongly affected by how busy the system is.