Random and Exogenous Variation in the Model

Random Sources of Variation

The random sources of variation are generated using pseudo-random number generators. The QSIM application provides a set of standard generators. These include:

Exponential, with mean $\lambda$ and density function
$f(x)=\lambda\exp^{-\lambda x}, { for } x \geq 0, \lambda \geq 0$
Nonhomogeneous Poisson, with rate parameter $\lambda(t)$ and density function
$f(x)=\frac{1}{\lambda(t)}\exp^{-x/\lambda(t)}, { for } x \geq 0, \lambda(t) \geq 0$
where $\lambda(t)$ is cyclic and continuous for all $t \geq 0$ with
$\lambda^*\equiv \sup_{t \geq 0}\lambda(t)$
Gamma, with parameters $\lambda$ and n and density function
$f(x)=\frac{x^{n-1}\exp^{-x/\lambda}}{\lambda^n\Gamma(n)}, { for } x \geq 0, \lambda \gt 0, n \gt 0$
Erlang, with parameters $\lambda$ and n and density function
$f(x)=\frac{x^{n-1}\exp^{-x/\lambda}}{\lambda^n\Gamma(n)}, { for } x \geq 0, \lambda \gt 0, n\epsilon Z^+$
Uniform, with parameter U and density function
$f(x)=\frac{1}U, { for } U \geq 0, 0 \leq x \lt U$
IUniform, with parameter U and density function
$f(x)=\frac{1}{\lfloor U\rfloor}, { for } U \geq 1, 0 \leq x \leq \lfloor U\rfloor, x \epsilon Z^+$
Deterministic, with parameter U and density function
f(x) = 1, for x = U

Each of these generators has a control panel for setting parameters. For example, if you pick Exponential from the list box in Figure 6.1 and then click the Parameters button, the exponential control panel in Figure 6.2 will be displayed. In this window, you set the inital seed value and the mean $\lambda$ .

Figure 6.2: The Exponential Control Panel

The seed value for each distribution is initialized automatically. You have the capability of changing this value. The next section tells you how you can control seed values.

Note that, by default, the Exponential mean in Figure 6.2, is set to 1. You can change the mean with the slider. The slider has a range of 0 to 10 for this parameter. If 10 is not large enough for the mean, you simply click in the display and type the mean that you want.

Controlling the Seed Values

Controlling Time Units

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