Running Terminating Simulations

Experiments involving terminating simulations are usually conducted by making several simulation runs, or replications, of the period of interest using a different random seed for each run. This procedure enables statistically independent and unbiased observations to be made on the system response over the period simulated. Statistics are often gathered on performance measures for successive intervals of time during the period.

For terminating simulations, we are usually interested in final production counts and changing patterns of behavior over time rather than the overall average behavior. It would be absurd, for example, to conclude that because two technicians are busy only an average of 40% during the day that only one technician is needed. This average measure reveals nothing about the utilization of the technicians during peak periods of the day. A more detailed report of waiting times during the entire work day may reveal that three technicians are needed to handle peak periods, whereas only one technician is necessary during off-peak hours. In this regard, Hoover and Perry (1990) note:

It is often suggested in the simulation literature that an overall performance be accumulated over the course of each replication of the simulation, ignoring the behavior of the systems at intermediate points in the simulation. We believe this is too simple an approach to collecting statistics when simulating a terminating system. It reminds us of the statistician who had his head in the refrigerator and feet in the oven, commenting that on the average he was quite comfortable.

For terminating simulations, the three important questions to answer in running the experiment are:

1. What should be the initial state of the model?

2. What is the terminating event or time?

3. How many replications will you make?

Many systems operate on a daily cycle, or, if a pattern occurs over a weeks time, the cycle is weekly. Some cycles may vary monthly or even annually. Cycles need not be repeating to be considered a cycle. Airlines, for example, may be interested in the start-up period of production during the introduction of a new airport which is a one-time occurrence.

The number of replications should be determined by the precision required for the output. If only a rough estimate of performance is being sought, three to five replications are sufficient. For greater precision, more replications should be made until a confidence interval with which you feel comfortable is achieved.