# Documentation

## Use Statistics to Understand SimEvents Models

### Statistics for Data Analysis

The purpose of creating a discrete-event simulation is often to improve understanding of the underlying system or guide decisions about the underlying system. Numerical results gathered during simulation can be important tools. For example:

• If you simulate the operation and maintenance of equipment on an assembly line, you might use the computed production and defect rates to help decide whether to change your maintenance schedule.

• If you simulate a communication bus under varying bus loads, you might use computed average delays in high- or low-priority messages to help determine whether a proposed architecture is viable.

When you design the statistical measures that you use to learn about the system, consider these questions:

• Which statistics are meaningful for your investigation or decision? For example, if you are trying to maximize efficiency, then what is an appropriate measure of efficiency in your system? As another example, does a mean give the best performance measure for your system, or is it also worthwhile to consider the proportion of samples in a given interval?

• How can you compute the desired statistics? For example, do you need to ignore any transient effects, does the choice of initial conditions matter, and what stopping criteria are appropriate for the simulation?

• To ensure sufficient confidence in the result, how many simulation runs do you need? One simulation run, no matter how long, is still a single sample and probably inadequate for valid statistical analysis.

For details concerning statistical analysis and variance reduction techniques, see the works [7], [4], [1], and [2].

### Statistics for Run-Time Control

Some systems rely on statistics to influence the dynamics. For example, a queuing system with discouraged arrivals has a feedback loop that adjusts the arrival rate throughout the simulation based on statistics reported by the queue and server.

When you create simulations that use statistical signals to control the dynamics, you must have access to the current values of the statistics at key times throughout the simulation, not just at the end of the simulation. Some questions to consider while designing your model are:

• Which statistics are meaningful, and how should they influence the dynamics of the system?

• How can you compute the desired statistics at the right times during the simulation? It is important to understand when SimEvents® blocks update each of their statistical outputs and when other blocks can access the updated values.

• Will small perturbations result in large changes in the system behavior? When using statistics to control the model, you might want to monitor those statistics or other statistics to check whether the system is undesirably sensitive to perturbations.

### Statistical Tools for Discrete-Event Simulation

The table lists components that SimEvents models commonly use to gather or compute statistics.

Statistical InformationAvailable Tools

Number of entities in a queue or server

n output signal from queue and server blocks

Utilization of a server

util output signal from Entity Server block

Number of entities that have departed from a block

Pending entity present in block

Number of entities arrived

a output signal from Entity Terminator block

Average wait

Average intergeneration time

w output signal from Entity Generator block

Average queue length

l output signal from Entity Queue block

Number of pending entities

np output signal from Entity Server block

Custom computation on event actions