## Initialization Bias in Steady-State Simulations

There are several methods of reducing the point estimator bias which is caused by using artificial and unrealistic initial conditions in a steady-state simulation.

1. Initialize the simulation in a state that is more representative of long-run conditions. E.g. use a set of real data as initial condition.

2. Divide the simulation into two phases, warm-up phase and steady state phase. Data collection doesn't start until the simulation passes the warm-up phase.

Consider the example on page 452 (Example 12.13)

• A set of 10 independent runs, each run was divided into 15 intervals. The data were listed in Table 12.5 on page 453.
• Typicall we calculate average within a run. Since the data collected in each run is most likely autocorrelated, a different method is used to calculate the average across the runs.
• Such averages are known as ensemble average.

Several issues:

1. Ensemble average will reveal a smoother and more precise trend as the number of replications, R, is increased.
2. Ensemble average can be smoothered further by plotting a moving average. In a moving average each plotted point is actually the average of several adjacent ensemble averages.
3. Cumulative averages become less variable as more data are averaged. Thus, it is expected that the curve at left side (the starting of the simulation) of the plotting is less smooth than the right side.
4. Simulation data, especially from queueing models, usually exhibits positive autocorrelation. The more correlation present, the longer it takes for the average to approach steady state.
5. In most simulation studies the analyst is interested in several measures such as queue length, waiting time, utilization, etc. Different performance measures may approach stead state at different rates. Thus it is important to examine each performance measure individidually for initialization bias and use a deletion point that is adequate for all of them.