Modeling Information Delays with Dispersion

In many cases, an information signal is dispersed, “smoothed” or “smeared” such that the output represents a weighted average of previous values for the input signal. (With no dispersion, the weight for the input value at t – Delay Time is one, and all other previous inputs have a weight of zero).

To specify that the information is dispersed, you must select either “Erlang n” or “Std. Deviation” from the Dispersion drop-list. These are two alternative ways to quantify the degree of dispersion in the signal.

If “Erlang n” is selected, you must enter a dimensionless value greater than or equal to 1. As n increases, the degree of dispersion decreases. As n goes to infinity, the dispersion goes to zero. The maximum amount of dispersion allowed is represented by n = 1.

If “Std. Deviation” is selected, you must enter a value with dimensions An output attribute for an element that defines the dimensionality (in terms of Length, Time and other fundamental dimensions) of the output. of time. The value must be greater than or equal to zero and less than or equal to the Delay Time. As the Std. Deviation decreases, the degree of dispersion decreases. When the Std. Deviation goes to zero, the dispersion goes to zero. The maximum amount of dispersion allowed is represented by Std. Deviation = Delay Time.

The Erlang n and the Std. Deviation are related by the following equation:

The figure below shows the response of an Information Delay A delay element that delays information signals, and does not enforce conservation of the signal. It is intended to be used to simulate delays in measuring, reporting, and/or responding to information. to a step function for various values of n:

Note that n = 1 (the highest level of dispersion allowed) is a special case referred to as exponential smoothing. In this case, the calculation carried out by the Information Delay element to compute its output is equivalent to exponentially weighting the previous values (i.e., the most recent value has the highest weight, and the weights of older values decrease exponentially). Exponential smoothing is a commonly used forecasting model.