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Signal Timing Design: Theory and Concepts

 
Saturation Flow Rate and Capacity

 Saturation Flow Rate

Saturation Flow Rate can be defined with the following scenario: Assume that an intersection’s approach signal were to stay green for an entire hour, and the traffic was as dense as could reasonably be expected. The number of vehicles that would pass through the intersection during that hour is the saturation flow rate.

Obviously, certain aspects of the traffic and the roadway will effect the saturation flow rate of your approach. If your approach has very narrow lanes, traffic will naturally provide longer gaps between vehicles, which will reduce your saturation flow rate. If you have large numbers of turning movements, or large numbers of trucks and busses, your saturation flow rate will be reduced. Put another way, the saturation flow rate (s) for a lane group is the maximum number of vehicles from that lane group that can pass through the intersection during one hour of continuous green under the prevailing traffic and roadway conditions. The saturation flow rate is normally given in terms of straight-through passenger cars per hour of green. Most design manuals and textbooks provide tables that give common values for trucks and turning movements in terms of passenger car units (pcu).

Determining the saturation flow rate can be a somewhat complicated matter. The saturation flow rate depends on roadway and traffic conditions, which can vary substantially from one region to another. It’s possible that someone in the area has already completed a measurement of the saturation flow rate for an approach similar to yours. If not, you'll need to measure it in the field. One other possibility, which is used quite frequently, is to assume an ideal value for the saturation flow rate and adjust it for the prevailing conditions using adjustment factors. A saturation flow rate of 1900 vehicles/hour/lane, which corresponds to a saturation headway of about 1.9 seconds, is a fairly common nominal value. Design manuals usually provide adjustment factors that take parameters such as lane-width, pedestrian traffic, and traffic composition into account.

Capacity

Capacity is an adjustment of the saturation flow rate that takes the real signal timing into account, since most signals are not allowed to permit the continuous movement of one phase for an hour. If your approach has 30 minutes of green per hour, you could deduce that the actual capacity of your approach is about half of the saturation flow rate. The capacity, therefore, is the maximum hourly flow of vehicles that can be discharged through the intersection from the lane group in question under the prevailing traffic, roadway, and signalization conditions. The formula for calculating capacity (c) is given below.

c = (g/C) s

Where:
c = capacity (pcu/hour)
g = Effective green time for the phase in question (sec)
C = Cycle length (sec)
s = Saturation flow rate (pcu/hour)

Capacity can be calculated on several levels, depending on the amount of information you want to obtain. You could calculate the capacity for each individual lane, or you could lump the lanes together and find the capacity of an entire approach. You need to decide what makes sense for your situation.

Capacity can be used as a reference to gauge the current operation of the intersection. For example, let us assume that you know the current flow rate for a lane group and you also know the capacity of that lane group. If the current flow rate is 10% of the capacity, you would be inclined to think that too much green time has been allocated to that particular lane group. You'll see other uses for capacity as you explore the remaining signal timing design concepts.