Understanding State Variables in GoldSim

Within a GoldSim model (actually, any dynamic model), there are fundamentally two types of outputs:

1. Outputs whose current value only depends on the current value of their element’s inputs ((i.e., they have no “memory”). These outputs themselves fall into one of two sub-categories:

o Those that represent unchanging input data (or direct functions of input data) and are therefore static, in that they only need to be computed at the beginning of the simulation and do not need to be recalculated every timestep. Examples include the outputs of Data elements and Stochastics (which are not being resampled).

o Those whose inputs change with time, and therefore need to be recalculated every timestep. Examples include the outputs of Expressions and Selectors whose inputs vary with time.

2. Outputs whose value is computed based on the historical value of the element’s inputs (as opposed to only being a function of the current value of the element’s inputs). These outputs can be thought of as having “memory” of what has happened before. The primary output of a Reservoir or a Pool is a classic example.

This second type of output is referred to as a state variable in GoldSim. State variables are typically the key system variables that you are interested in predicting. Together, the state variables define the predicted state of the system at any time in the future. Examples of state variables include the volume of water in a pond, the amount of money in an account, the status (on/off/failed) of a piece of equipment, and the number of times a certain event has occurred.

All state variables have, by definition, an initial value (e.g., for Integrators, Reservoirs and Pools, the initial value is explicitly specified). This allows the outputs to be computed when there are no historical input values available (e.g., at the start of simulation).

All state variables have “memory”; that is, their value at time t is a function of their value at time t - ∆t. Furthermore, state variables can change during a simulation in two different ways:

• Some state variables are intrinsically a function of time. That is, every timestep, they may change because they are inherently defined with respect to time. Integrators, Reservoirs and Pools are examples of this. Since these elements fundamentally solve time integrals, whenever the simulation time changes, by definition they must be updated.

• Some state variables can be triggered by or respond to other elements in the model, and in turn, change their value. A Status element is a good example of this.

Some state variables may change due to just one of these mechanisms, while others may potentially change due to both. For example, Status elements can only change by the second mechanism; Reservoirs can change due to both.

Note that based on whether or not a particular state variable can change due to the second mechanism listed above, it falls into one of these two categories:

1. Its value at time t is completely determined by its value (and the inputs) at time t - ∆t.

2. Its value at time t is determined by its value (and the inputs) at time t - ∆t, but can also be further modified by its inputs at time t.

Most state variables fall into the second category.

The most common state variables are the primary outputs of stocks (Integrators, Reservoirs and Pools). A number of other elements, however, also have outputs which are state variables, and these are summarized in the table below.

Element	Output
Integrator	Current Value
Pool	Current Value (Quantity)
Pool	Is_Full
Reservoir	Current Value
Reservoir	Is_Full
Stochastic	Current Value
	Probability Density
	Cumulative Probability
Script	Result (primary output)
Extrema	Current Value
Status	Current Status
Decision	Last Decision
Milestone	Completion Status
	Date of Completion
	Elapsed Time of Completion
Timed Event Generator	Cumulative Number Emitted
Triggered Event Generator	Cumulative Number Emitted
Discrete Change	Cumulative Number Emitted
Information Delay	Current Value
Material Delay	Current Value
Material Delay	Amount in Transit
Event Delay	Cumulative Number Emitted
	Number in Transit
	Number in Queue
	Mean Time for Emitted Events
	Current Service Time
Discrete Change Delay	Cumulative Number Emitted
	Number in Transit
	Number in Queue
Conditional Container	Activity Status
Conditional Container	Completion Status
Previous Value	Previous value of input
Time Series	Current Value
History Generator	Current Value

Outputs listed in bold fall into category #1 above (i.e., they can never be impacted by inputs from the current timestep).

The icons for state variables are indicated in browsers (e.g., output ports) by showing a vertical line to the left of the output triangle:

Reservoir1 (the primary output) and Is_Full are state variables.

Note: In addition to the elements listed above, a number of elements in GoldSim’s extension modules also have outputs that are state variables.