## Info

Real systems

Simulated systems

Real people Simulated people

Live simulation Smart systems

Virtual simulation Constructive simulation

When simulating a complex assemblage of independent, but interconnected, systems, it is common to refer to such an assemblage as a "system-of-systems." Simulating the performance of such an assemblage is often referred to as "end-to-end" simulation. The "state" of a system is defined by the collection of variables necessary to describe that system at any given time.

Simulations are differentiated at three levels of system representations: static versus dynamic; deterministic versus stochastic; and continuous versus discrete. A static simulation represents a system state in which time is not a variable. Conversely, a dynamic simulation varies as a function of time. A deterministic simulation produces completely predictable values whereas a stochastic simulation produces values that must be represented by statistical variables (e.g. means and variances). A continuous simulation produces state variables that change continuously with changes in time while a discrete simulation produces values that change in a stepwise fashion as a function of time (Law and Kelton, 1991).

Different mathematical approaches are used depending on the type of simulation employed. For example, continuous-system simulations are modeled using differential equations while time-stepped simulations are modeled using discrete-time approaches. Event-based simulations are modeled as discrete events.

Law and Kelton (1991: chapter 12) provide a comprehensive introduction to the use of statistical experimental design and optimization techniques in simulation. Specifically, experimental design provides a way of deciding before any runs are made which particular configurations should be simulated so that the desired information can be obtained with the least amount of simulation. The term "design of experiment" (DOE) is sometimes used in the literature in reference to this process. Design of experiment is particularly important when simulation is used to evaluate (or trade) alternative system configurations.

To structure subsequent discussions, the four hierarchical levels of simulation (engineering, engagement, mission and theater) are first reviewed in Section 12.2. Next, simulation infrastructure is discussed in Section 12.3 using examples drawn from defense-related activities. Section 12.4 discusses the high-level architecture (HLA), currently the highest priority effort within the defense modeling and simulation community. The role of test-beds is described in Section 12.5. Finally, a survey of current applications in Section 12.6 provides specific examples of generally accepted approaches and common practices.

### 12.2 Hierarchical levels

As previously mentioned in Chapter 1, simulation in support of naval applications can be decomposed into four fundamental levels: engineering, engagement, mission and theater. Table 12.2 summarizes the outputs and

Table 12.2 Four principal levels of simulation for naval applications

Level

Output

General applications

Theater

Force dynamics

Evaluate force structures

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