Exponential smoothing of detector occupancy rates

You can use exponential smoothing to smooth the occupancy rate of a detector. This is necessary as detectors are either fully occupied or not occupied and thus do not provide sufficient information for signal control decisions.

Vissim calculates the exponentially smoothed occupancy rate using the following equation:

The occupancy rate from the last time interval of the signal control, which was determined depending on the frequency of the signal controller, is also taken into account. Thereby the following applies:

s(t)	new, exponentially smoothed occupancy rate
s(t-1)	old, exponentially smoothed occupancy rate, determined depending on the frequency of the signal controller
x	currently measured, non-smoothed internal occupancy rate between 0 and 1
α	Smoothing factor [0 to 1], which can be entered for Increase and Decrease
i	Internal indicator from new occupancy rate s(t) and old occupancy rate s(t-1)

After that, the new exponentially smoothed value is the weighted average of the currently measured non-smoothed occupancy rate and the smoothed occupancy rate from the last time interval of the signal control.

The new detector occupancy rate is weighted with α.

The old, smoothed value is weighted with (1 - α).

In Vissim, you can use the following attributes to enter different values for α (Attributes of detectors):

• Increase: For increasing x values (for x > s(t-1))
• Decrease: For decreasing x values (for x < s(t-1))

The exponentially smoothed occupancy rate represents a kind of a floating average of the detected values of all previous time steps. Thereby the most current values are weighted the strongest. With α = 1, there is no smoothing. The equation then equals the new detector value x.

In the Vissim network, in the attribute list Detectors, you can show values of the attributes Occupancy rate (OccupRate) in % and Occupancy (Occup) i (Editing attributes in a list).