# Chapter 5 Statistical Analysis for Infinite Horizon Simulation Models

LEARNING OBJECTIVES

• To understand the concept of steady state analysis and the implications of modeling an infinite horizon system.

• To be able to analyze infinite horizon simulations via the method of replication-deletion

• To be able to analyze infinite horizon simulations via the method of batch means

• To be able to perform sequential sampling for an infinite horizon model

• To be able to apply verification and validation methods

This chapter discusses how to plan and analyze infinite horizon simulations. When analyzing infinite horizon simulations, the primary difficulty is the nature of observations from within a replication. In the finite horizon case, the statistical analysis is based on three basic requirements:

1. Observations are independent

2. Observations are sampled from identical distributions

3. Observations are drawn from a normal distribution (or enough observations are present to invoke the central limit theorem)

In Chapter 3, these requirements were met by performing independent replications of the simulation to generate a random sample. Simulating independent replications is natural when performing an analysis of a finite horizon model. In the case of a finite horizon model, there are very well determined initial and ending conditions. Initial conditions refer to the starting conditions for the model, i.e. whether or not the system starts "empty and idle". The challenge of performing an infinite horizon simulation is that there are, in essence, no initial and ending conditions. We often call infinite horizon simulation by the term steady state simulation. This is because, in this context, we want to measure the performance of the system after a long time (i.e. under steady state conditions). The effect of initial conditions on steady state performance measures will be discussed in this chapter.

In a direct sense, the outputs from within a replication do not satisfy the requirements of producing a random sample (IID observations); however, certain procedures can be imposed on the manner in which the observations are gathered to ensure that these statistical assumptions are not grossly violated. The following section will first explain why within replication observations typically violate these assumptions and then we will explore some methods for mitigating the violations within the context of infinite horizon simulations.

The chapter ends with an illustration of methods to verify and validate a simulation model. The analysis will rely on concepts of queueing theory (see Appendix C) and the use of analytical formulas that apply to steady state queueing systems.