## 3.7 Summary

This chapter described many of the statistical aspects of simulation that will be typically encountered when performing a simulation study. An important aspect of performing a correct simulation analysis is to understand the type of data associated with the performance measures (time-persistent versus tally-based) and how to collect/analyze such data. Then in your modeling you will be faced with specifying the time horizon of your simulation. Most situations involve finite-horizons, which are fortunately easy to analyze via the method of replications. This allows a random sample to be formed across replications and to analyze the simulation output via traditional statistical techniques.

In the case of infinite horizon simulations, things are more complicated. You must first analyze the effect of any warm up period on the performance measures and decide whether you should use the method of replication-deletion or the method of batch means. These topics will be covered in Chapter 5.

This chapter also provided additional examples of the following Arena modules:

- CREATE
- ASSIGN
- PROCESS
- SEIZE, DELAY, RELEASE option
- DELAY option

- DECIDE
- 2 way with condition
- N-way with condition
- 2 way with chance

- GOTO LABEL
- LABEL
- RECORD
- expression option
- time interval option

- Statistical collection
- OUTPUT
- TIME PERSISTENT
- TALLY
- FREQUENCIES

A RECORD module is placed within the model window. It is used to record observations at particular event times as denote by where the module is placed within the flow path of the entity within the model. The RECORD module using the “expression” option will compute statistics on the value computed by the expression. The critical thing to remember about the RECORD module is that it is executed when an entity passes through it. Thus, what it observes (records) will be dependent upon where it is placed and when it is executed.

The STATISTIC module is used to define and collect additional statistics that occur during a simulation. The STATISTIC module also allows for the definition of files to store observed values. First, it allows the modeler to pre-define Tallies and Counters, which are what RECORD modules use. This is similar to using the RESOURCE module to define resources that are used in the model window, or pre-defining variables or attributes before using them in the model. Finally, the STATISTIC module allows the user to define OUTPUT statistics. These work in a similar fashion as how RECORD works, except the expression is *observed one time, at the end of the replication*. While a RECORD module can observe values at any simulation time, the OUTPUT statistic option of the STATISTIC module can only observe values at the end of a replication.

The STATISTC module also allows for the definition of Time Persistent statistical collection on variables defined in the model. This functionality is the same as checking the “collect statistics” box when defining a variable; however, it also provides additional functionality. First, the modeler can provide their own name for the time persistent statistic and may choose to save the data into a file. Secondly, through the STATISTIC module, the modeler can define periods of time over which statistics can be collected on a variable. This is very useful in simulation situations that have time-varying inputs. Finally, the STATISTIC module allows for the definition of FREQUENCIES to provide finer detailed collect of time persisting variables in states or categories.

This chapter has covered almost all of the most useful aspects of collecting statistics from your simulation model. As a final note, there are other statistics that are automatically collected by Arena, some of which do not add much value to the analysis. For example, when you run your model and view the category reports, the very first item that you see is summary about the number of entities in and out of the model. I strongly recommend **ignoring** these numbers. They are pretty much useless unless you commit to using Entity Types, for which I have never found a strong use case, except for applications involving activity based costing (See Appendix D).

Now that you have a solid understanding of how to program and model in Arena and how to analyze your results, you are ready to explore the application of simulation to process modeling situations involving more complex systems. These systems form the building blocks for modeling systems in manufacturing, transportation, and service industries.