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. Exponential smoothing allows you to calculate the occupancy rate with help of the following equation, using the last t seconds:

Thereby the following applies:

s(t)	new, exponentially smoothed value
s(t-1)	old, exponentially smoothed value (1 second ago)
x	new detector value
α	Smoothing factor [0 to 1]

This means the new, exponentially smoothed value is the weighted average of the new, detected value and the exponentially smoothed value after the last simulation second.

The new detector occupancy rate is weighted with alpha.

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

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

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